Although he does look kind of skinny, I think thin works for Peter Parker/Spidey as well. Still muscular, mind you, but he doesn't need to be "buff" either. As for the costume, I like what I see - at least so far. I really liked the previous movie costume, but I can understand why they would want to change it up and make a "break" from those previous movies since this is supposed to be a reboot. As long as the rest of the costume doesn't get too wacky, and the mask/eyes of the suit look good, I'll be happy.
As far as the web shooters, there is speculation that on the enlarged version of this photo you can see something on his wrist that look very mechanical web-shooter-like. That would be cool. I will say, I think that Andrew Garfield, at least from the very little we've seen so far, does look the part (Peter Parker at least) pretty well.