Original question, thanks for asking!
I look for a bit of padding (depends on the bars how much I really need -- a good bar has a curve that matches my hand, a bad bar needs a lot more padding). Not too much padding, though, or I don't feel like I've got a good grip. Good cork tape is OK on the former, not the latter IME.
I prefer to buy in person, so I can rub my finger across the tiny opening in the box. I mail ordered some once -- awful stuff, slick plastic outside, felt like my hands were sliding around every time I gripped the bar. And not too tacky, pine tar need not apply.