If you take pride in yourself and how you look, I don't see a problem with what you wear. Typically the polos and button ups look nicer and more dressy. As long as your tees don't have holes, stains or stretched out collars - I think those are fine too
Depends on the kind of shirt. I can tell you right now that I don't like guys in really baggy shirts and pants around their ankles. Please don't do the gangsta look, it looks awful. A nice fitting shirt is better, maybe with v-neck, those are hot. I love button downs, especially blue ones. Polo shirts are OK, I guess.
It's better to wear what makes you feel more comfortable, confidence will do more for you than any shirt can.
A lot of girls will say their favorite look is jeans and a t shirt.
If you have a good body wear t shirts in the right size and they should look good.
If you do not have a good body, t-shirts are actually pretty unforgiving. They have no structure. An untucked polo shirt - again in the right size- draws more attention to your face and creates some structure. If you're chubby, you probably would look better in them.
That may be true in respect to t-shirts with logos of things you don't know much about. For example, guys who wear skater shirts and don't skate. It doesn't bother me personally, but I prefer not to do it myself.
I usually wear a plain t-shirt or v-neck. No logos, etc. I'll wear a polo when going out and a button up for certain events.
T-shirts will never get old or make you seem immature.