What Perks/Guns/Attachments naturally work well together?
Lightweight Pro + Ninja Pro + Marathon Pro + UMP with silencer is the best if you want to go silent and move quickly around the map.
Sleight of Hand Pro + Stopping Power Pro + Steady Aim plus a baretta .cal or an intervention is the perfect sniper "class". You need the stopping power to deal extra damage indifferent of the body part you are aiming at.
When making a choice, what important things should I consider?
What type of map are you playing, what type of game and really what type of player are you (sniper, stealth, commando, defender, etc)
Don't worry about players with higher levels than you, trust me, in this game levels aren't direct proportional with player skill.
How are these choices potentially affected by gameplay type or map pool ?
I've answered partially above, all in all it depends on your skill and the weapon you feel the most comfortable with. If you are a sniper and you feel that the intervention is your gun no matter the map or game you will be good at it.
How does level play a role?
Levels are there for getting upgrades and camos. Also you get attachments by using a specific type of weapons. You get your perks upgraded by using a specific perk over and over.
In any case to get to upgrade some attachments faster use the default classes that have the goodies unlocked. E.G Tactical knife can be unlocked by playing with the First Recon class, it's a short way to get it done.
EDIT: First Build: The UMP has the best recoil in the game in my honest opinion, you aim smoother and there is a very slim chance that your cross-hair will wiggle too much. The Perk combination is obvious move faster and be undetected. Ninja Pro silences your footsteps.
Second Build: A sniper rifle has a high recoil so you need to reload fast to make each shot count. With Steady Aim you can keep your breath for an extensive period of time. Stopping Power Pro will enhance the damage dealt by half i believe, so even if you hit the body for example it will be a a kill and not a hit marker.
I forgot the secondary weapons, never used them that much, but if you want to be sure you get the guy before you restock on your primary get a shotgun, more specifically the Spas-12.