You should own a snap-up, or button up shirt that's a little too big for you, that's not offensive, or some crazy color. Something from Target is fine. This shirt will have one purpose and one purpose only.
It is your On Set Shirt. Yeah, I capitalized, it's a proper name.
I'm not saying that you have to where this shirt TO the set, but it's going to help you out once you get ON set. Here's why.
Say you're sitting in the make-up chair, and the hair person just finished about 20 minutes (if your a guy) or an hours (if your a gal) of work. You then go over to wardrobe to get your stuff. What happens then? Before you can put your wardrobe on, you've got to take your t-shirt off...over your head.
You're about to ruin someone's work, and they're going to have to come touch you up. Before the shoot even starts.
Once you get to set, and have made your impression with you're awesome sense of style. Change into your on-set shirt before sitting down in the make up chair. When you're done, and it's time to change, you don't have to worry about messing up someone else's hard work as the first thing you do on set.
There's another reason you should have an onset shirt, we're not done yet.