This probably isn't the best thing for my first post on Escapist, but I had to come out of lurking to say this:
In the words of the Heavy: Cry some moar.
All of us were new and were getting backstabbed/headshotted when we started.
With that out of the way, I'll give some actual advice.
Rule 1 when playing TF2: EVERYTHING is a Spy. EVERYTHING. Spycheck EVERYONE. Even if it's obvious they're not a Spy (revved up Heavy, scoped-in Sniper, etc.) just get into the habit of it. Every 10 seconds or so, turn around. Even when your disguised.
Not having a mic is a non-issue. I don't have a mic and was in the top three of the past few games I've played.
Even though you like to play Spy, if you're new, DON'T. Spy requires extensive knowledge of the game, maps, modes, and (most importantly) classes. You need to know how each class is supposed to act, where they are likely to be, and so on. Some advice as Spy, though: If you ignore spychecks from non-Pyros (since you will burn your team color) most players will move on. Just think about what you do when your teammates are checking you.
While you are getting used to the different classes and maps, play Medic (even if it doesn't sound like you like that), Heavy, and especially Pyro. Another relatively easy one is Engineer on a CTF map. Just hide in a corner of the Intel room and build up and spycheck everyone that comes in with at least three shotgun blasts, preferably the whole clip. Also, don't go for melee kills as the Demo until you get a Chargin' Targe.
But the best advice I can give you is find a friendly server and spend time reading the Wiki. There is A LOT of useful information there. If you don't want to "waste your time," just read the Class Strategies part. (Also, it helps if you just play to have fun and not "to win." Personally that just causes me RAEG.)
Anyway, that's my advice. Feel free to ignore or embrace it. Once you get some drops and a friendly server, it'll get better.