nike Dri fit tops are great, they and most other brands have something called wicking which takes the sweat away from your skin. I started out 4 years ago with loads of old cotton t shirts and have ditched them all for so called technical running tops.
i think Karrimor and Decathlon are the cheap entry brands or look on the linked online retailers from RW forums, most have old lines in clearance.
If you can already run for 12 mins on the treadmill, you're going to find couch to 5k really dull if you start at the beginning.
I'd suggest you run 10 minutes away from your house, walk back for 2 minutes and see if you can run/walk the rest of the trip home. You can extend the out bound leg a couple of minutes each week and then you'd be up to a 5k total in about 4 or 5 weeks.