What’s the best way to grip a straight bar when doing bench press, thumbs wrapped around the bar or with your thumbs on the same side of the bar as your fingers?

The “right way” is whatever way you are most comfortable with. However, I highly suggest you bench with your thumbs around the bar. This is a much safer and more secure grip.

I see many lifters using the thumb in back method. There is no advantage to this at all, and it’s a bad habit to get into. I imagine that just about everyone has seen someone drop the bar on their chest when benching. I’ve seen it many times. I’ve never seen this happen when someone used a proper grip with their thumb around the bar. With this grip, it will not happen.

There is no strength or leverage advantage with either method. Some people find the thumb in back method more comfortable, but mostly the use of this grip is born out of being taught this bad habit early in their lifting career. Habits are hard to break, but this is definitely one you should work to get rid of.

I highly recommend getting comfortable and confident gripping the bar correctly.