First, money is fairly easy come by in this game, especially with the right hacking skills unlocked early on. That said, buy better weapons as you see yourself needing them.
Along with that, upgrade the appropriate skills as you use/plan to use them for your personal play style. I can't really give you tips on how to spend your skill points since I'm not sure how you like to play the game. I'm only suggesting there are some that likely suit your style and make fighting easier.
Don't underestimate the effectiveness of grenades and other explosives. Try to keep yourself stocked up. Later on when you encounter the large riot armor enemies, proximity bombs are your friends as you can take one out in a couple bombs (depending on difficulty probably, I played on normal). The important thing here is you always want to keep stocked up on crafting components in case you run out in the heat of a difficult battle. So don't be afraid to visit the pawn shops to buy supplies, they cost pocket change.
Cover based combat in this game is not all about the gunplay:
Hack the surroundings to your advantage. Wait until an enemy or 2 walk up to those power box thingys and explode them. Is an enemy hiding behind cover that you can hack away? Remove it. Can you activate some cover for yourself? Do it. Some enemies even have hackable grenades (these don't always work). Many times there are surrounding cameras you can access that can give you better views in these types of situations (although if spotted, be sure you're in a safe enough spot/not being flanked. Often times you can see yourself in these cameras).
Running away might seem like a bad option but it often isn't in this game. Especially considering a lot of the shootout happen in fairly "circular arenas" (I'm using that very loosely), you might find that the best option is to retreat a little and circle around to some new cover. It will buy you time and keep some distance between some of the baddies.
A good tactic to pair with that last paragraph is to use your melee attacks when you can. If you need new cover and there is a enemy behind some cover you need, beat the crap out of him when he is reloading or recently ducking behind cover. Cover takedowns are also super effective, especially if you're still unseen. That brings me to another good point...
Stay stealthy when possible. It will allow you to take out as many guys as possible before the poo hits the fan. This is a tactic I use frequently. Your silenced pistol is basically one of your best friends throughout the game. It's also fairly easy to get headshots if you haven't been seen yet so take a few isolated guys out. Stealth is not overrated in this game.
You mention you enjoy cover based shooting so I assume you're familiar with this tip, but do not leave your cover unless you absolutely need to (or you're transitioning cover). Standing in the open will get you killed. You aren't a CoD bullet sponge. While in cover, don't get impatient. Aim for headshots. Know where your weapon will be pointing when you peek out from your cover and this should be very easy (don't bother with shooting blindly from cover 97% of the time).
And the last point that comes to mind:
Pay attention to the type of enemies you're facing. If you haven't been seen yet, hack cameras and investigate your enemies. Don't set off enemies grenades all willy-nilly. Take out the ones who call for backup first, always. Then start setting off the explody bad guys when you're ready to start the fight, following the above tips to avoid death.