I'd just lay it over a clean chair and let it dry. I wouldn't hang it wet because then you could potentially stretch it out or leave marks. You could also put it in the dryer on gentle warm. The choice is yours young grasshopper.
It doesn't affect a crew neck or tee to hang them after they are dry does it? Or should the be folded and kept in a drawer after drying?
No not at all...you'd be fine. I'm just saying if any heavy clothes are wet and you put a hanger on them, the weight from the heavy wet material will pull down and the shoulders could get hanger marks. Just a rule of gravity more than anything.