As someone that's made many a fashion faux pas in my younger days, I can proudly say that I've never worn a vest with a tshirt. I second everything that kodave says and unless you're planning on having a hipster-like look, stay away from vests unless you're wearing a button down collared shirt that has a European slim cut with a vest fitted to match. This is assuming you have the body shape to pull it off.

Pro-tip: Skip Men's Warehouse and find a K&G. Better brands at Men's Warehouse prices...sometimes even better prices. Don't mistake brand names for quality though; it's usually just an indicator of the type of cut a suit has as they tend to have more of a modern cut.