Definitely do not use a shirt. You want tricept strength do weighted dips, skull crushers, tri extentions, close grip bench, etc. A shirt would do nothing for you. As a matter a fact I don't even think you would be able to get the bar to touch your chest with a shirt on.
When you hit the gym strart with bench then hit your tris, lats, upper back, and chest. In that order. Those are the muscles you want to foucus on if you want to increase your bench. Make sure your form in perfect before moving up weight. Don't let pride get the best of you and try to show off. It will either hurt you or set you back in the long run.