You're in for a real treat with this game!
Too Long; Didn't Read
This is kind of a long answer. My tl;dr version is: play a decker, choose the default decker settings during character creation, then put most of your karma points into intelligence, decking, and ESP control for the rest of the game, with some points in quickness, ranged combat, pistols and dodge to round you out for combat situations. Buy better decks and stronger programs whenever you can afford to.
Trouble With The First Mission - your first character might actually have been fine, and this part explains why.
Recommended First Time Build - why I'm recommending a decker.
Alternative Builds - other options based on the preferences you mentioned.
Available Companions - info about what roles are covered by the story companions in the game.
Spending Karma - info about spending your karma effectively.
Trouble With The First Mission
Having a bit of trouble with the first mission doesn't necessarily mean you've got a bad character build. You didn't mention what kind of build you ended up choosing, so I can't offer direct advice on that, but it's worth keeping in mind.
There's at least one fight in the first mission that's unusually difficult, for story-related reasons.
If you don't mind spoilers for the end of the first mission, here's some more information about why it's difficult:
The Ork security captain that you face is much more powerful than the other enemies you will face early in the game. Your main goal in the fight where he turns up is just to survive long enough to escape. It's totally fine if you can't take him on. If you happen to be particularly strong or lucky with your attacks it's possible to force him to retreat, but it doesn't really change anything about the outcome of the mission.
Recommended First Time Build
I think a decker makes an excellent choice for a first playthrough of Shadowrun: Dragonfall. It's also relatively consistent with the preferences you expressed.
Deckers get lots to do. It's easy to feel like your character is at the center of things when you play a decker. I think this is even more true of Dragonfall specifically (compared with Shadowrun Returns and Shadowrun: Hong Kong).
Lots of other RPG settings don't have characters that are much like deckers, so you really get to immerse yourself in the Shadowrun experience.
You still get to experience something of a "Summoner" role. You can summon Expert System Programs to help you in the Matrix (cyberspace/hacking), and you can have a drone for help during regular combat. My recommendation would be to ignore the drone skills and focus on Decking and ESP Control, but more on that in the Spending Karma section later on in this answer.
These two extra reasons contain spoilers for the early part of the story (things that happen in the first few missions):
There's a kind of poetic symmetry in being able to directly replace Monika's role in the team after her death during the first mission. I played a decker on my first time through the game and this aspect really added to story/roleplaying enjoyment for me.
The story companion who's a decker shows up towards the end of the second mission and he's kind of a jerk. You might be glad of a reason to avoid spending much time with him. More details on his pros and cons in the Available Companions section later on in this answer.
Here are some suggestions based off the character types you mentioning enjoying from other RPGs:
Dragonfall has a Mage archetype. Mages are very useful in combat. They're good damage dealers, and unlike most other RPGs they're also the archetype that has the healing spells.
Assuming the sideline summoning aspects of the decker weren't to your taste, the true summoner archetype in Dragonfall is the shaman. You can focus on spirit summoning and spirit control, and as a bonus your high charisma will give you lots of extra options in conversations due to knowing extra "etiquettes".
If you like rangers because of their archery, a street samurai with an emphasis on ranged combat is a good choice. It's a very powerful character type in combat, though it might feel a bit one-dimensional the rest of the time. Focus on Pistols if you like having special shots, or Rifles for raw damage output. I don't recommend Shotguns for your first time through, because their relatively short range and area-effect damage make them much more sensitive to your party positioning choices. SMGs are also a bit trickier to use really well.
There are four main story companions available from early in the game, and between them they cover all the critical roles in your party. This means you can safely choose any build you like and be confident that the story companions will fit around you. There's also one extra companion you can get relatively late in the game compared to the others.
Since the standard party size is 4, generally you will leave behind the companion which is closest to you in abilities and then take the other three.
You also have the option of hiring mercenary companions to fill specific roles in specific missions. This costs money, but in general there's plenty of money available in Dragonfall. They have less personality than the main story companions though, so in general I would only recommend mercenaries for when you're replaying the game (perhaps for the third or fourth time!) and want some extra variety.
If you don't mind spoilers about the identities and general capabilities of the story companions, there is more information hidden by spoiler tags below. I haven't spoiled anything about their storylines.
Eiger, from the first mission. If you choose all the upgrades from her sniper tree she becomes very powerful, in a way that I think helps a lot for a first-time player of the game. Her story mission can be a bit tricky depending on what kind of character you have. Save beforehand so you can try again with more drugs if needed. :)
Glory, also from the first mission. She has options for pistol upgrades too but I think the melee stuff is much stronger. She's great for bringing down armored enemies, and her high biotech skills makes her good with medkits. You don't have to pay for the medkits she brings with her, so don't hesitate to use them up when folks get hurt. Don't forget to use her adrenal pump ability!
Dietrich, also from the first mission. He's good for hasting, healing, and general support. He's a bit more of a generalist than the others so he isn't a major powerhouse at any particular thing. He's one of the easier companions to do without, especially if you're a shaman or a mage yourself. Haste is very strong though. Eiger and Glory both do really well when hasted, as might your own character if you're a combat specialist of some kind.
Blitz, available at the end of the second mission. Most people I've talked about the game with find him the least likeable companion, and that was true for me as well. He has his own special drone you can find during the same mission you meet him, but I didn't find it to be all that strong, at least not on hard mode - it's a bit of a bullet magnet. On the plus side, I think Blitz's personal mission is the most interesting one in the game. It has a somewhat unusual structure and I found it to be a lot of fun. If you play a decker in your first game, he's probably a good character to ignore and then pick up during your second game for variety's sake. (I think Dragonfall is definitely worth at least two playthroughs.)
Later utility companion (this is extra spoilery compared to the others, including arguably some story points):
Monika's dog, Dante, eventually becomes a companion too. He's not available until much later in the game compared to the others though. You need to make friends with him a bit during the early parts of the game to make sure he's available later. He's good against armored enemies and for doing lots of damage. He makes a good replacement for either Dietrich or Glory. Make sure to buy him some extra spells to complement the ones he comes with.
First of all, feel free to start off with one of the pre-configured archetypes from the character selection screen. They're all fine, and generally speaking they're well-rounded enough that for the rest of the game you can focus on putting points into a few things you want to be really good at and trust that the rest of your character traits are "good enough" to get away with.
Secondly, don't be afraid to save up your karma, especially if you're getting through the missions without too much trouble. Then when you run up against a problem, or you find some cool new equipment that has specific stat requirements, you can spend your saved up karma to handle the situation immediately. The reverse is true with companions though - choose their new abilities as soon as they level up, there's nothing to be gained from waiting.
I like to take intelligence 2 and biotech 2 with all my characters just for the enemy hit point display. In general I recommend avoiding biotech above level 2 though, even if you have higher intelligence because of being a decker or rigger.
To be really good at a particular role you generally need to put a lot of points into at least three things. For example, as a decker I recommend Intelligence, Decking, and ESP Control (I must respectfully disagree with the commenter saying that ESPs aren't good value). As a ranged combat type I recommend Quickness, Ranged Combat, and then either Pistols or Rifles. As a summoner shaman it's Charisma, Spirit Summoning and Spirit Control.
Keep the levels roughly the same for all three, except if you need to increase a specific stat in order to use a juicy new piece of gear you just found.
If your main three things aren't combat related, "splash" a smaller number of karma points into a damage source. If you're a decker, take some quickness, ranged weapons, and pistol skill to round yourself out. You can become quite effective for a relatively small amount of karma, and if you find yourself getting hit too much you can take a few points in Dodge, which is also in the quickness section. Getting some cyberware is also good for making a decker better in combat - in general you won't need it to help your decking.
If you're a summoner shaman then you should probably take some willpower and mage skills for a damage boost. This also gives you access to some healing. Cyberware interferes with your spellcasting so it's harder to get good at ranged combat as a damage source. Your summoned spirits are actually really strong in combat, but they're a bit less reliable and more situational than other damage sources so it's good to have something to fall back to.
Avoid melee unless your whole character is built around it. You won't be all that effective with only a moderate amount of points in melee, and your character will be much more likely to take damage due to trying to get close to the enemy.
If your main set of three things is combat related, it doesn't actually matter that much where your extra points go. Pick things that seem like they might help with a weakness you're having trouble with, or that seem like they might be fun. Putting enough points into charisma to get an extra social etiquette is always a good fallback option.
Thanks for reading! I hope you and everyone else reading this answer has a great time with Shadowrun: Dragonfall. It's truly one of the great RPGs!