Well when it comes to soldering I hear a soldering iron works pretty well.. Or so i'm told.. And solder is also rumored to work well with the iron, who knew?
Anyway I think a smaller tip would be good.. The guys will tell you what size to get.. I really don't remember the gauge.
http://www.aaroncake.net/electronics/solder.htm
There's a link that goes over the basics.. Also I suggest you practice quite a bit before you go at your box. Even if the xbox isn't as difficult as the ps2 it still isn't a cakewalk to a virgin solderer.. You may get frustrated easily if you don't get a feel for it.. Get some scrap wire strip the end and practice coating it with solder.. and make it look as pretty as you can..
Wait for the other guys to throw in their two cents. I'm sure they can give you plenty of tips.
Oh and sorry about the sarcasm.. just got off work.. and I realized I hate my life