You get rid of bandaged with a doctor bag, but if you're completely healed except for the bandaged modifier, you'll have to take some damage first and then patch yourself up with the doc bag.
My current team at the last mission :
Hell Patrol - Now concentrated solely on Energy Weapons
Stoma - Got 'im pretty early and concentrated on Big guns, now he has +200 big guns skill and is an extremely good shot, and his natural strengh of 10, his 2 carry weight perks and adv power armor make his carry weight astronomical. He was UBER-USEFUL for salvaging enemy weapons with his str of 10.
Some Chick I forgot the name of : I got her pretty late in the game, I think she's ranked Paladin Commander, she's my second energy weapons person, much more effective against robots. I used to have Stein in this place for my shotgunner/sniper/heavy weapons person, but his strength is pitiful for a heavy weapons guy (he couldn't even use miniguns), his small guns skill was only around 140, and even though right before I dumped him I gave him the weapons handling perk, I wasn't about to forgive him for all those bullets in the back and extra concussions that are the biproduct of using a heavy weapons gun in CTB mode. After the supermutant part I found no real use for another sniper added to my other 3, or a 2nd heavyweapons guy.
Farsight and Rebecca: Both snipers, both currently have insanely high small guns skill. I use Rebecca for my lockpicking, too.
Stich : He's got fairly good doctoring skills, and with his good skill point advancement his small guns skill is even better than rebecca's and farsights (he isn't as good a sniper though, do to his average perception), and I use him for sniping and shotgunning.
In short, I mostly prefer to catch 'em young and train em the way you like them, as I still have the original 2 teammates from mission 1, and 2 of the others can be recruited very early. I've never had a trapper in my party, though, all the tricks and traps books have raised my trapping skill to above 100.