First on the list for me is how they look. Not gonna try to specify what they need to look like; there's a lot of things I do like and a lot of things I don't. But the visual appearance is make-or-break for me; I'll put up with a lot of flaws for something I find attractive, and be flat-out uninterested in otherwise top-quality chips if they don't look right.
After that is feel, which encompasses a lot of things: weight, hardness, slipperiness, sharpness of edges, the specific sounds they make when hitting each other or when hitting the table (yes, sound for me is part of "feel"). Here's the thing, though: every chip feels different, often
very different, and the way they feel is important... but I like the way
all chips feel, with very few exceptions. I like some better than others, but in general, I just think that
poker chips feel great and I'm happy to play with any of them, treasuring each for its own characteristics.
Slipperiness is very important to some people, but not so much to me. Yes, some chips are harder to stack and more awkward to handle because they are especially slippery, but I haven't yet found any that are so slick that they're impractical or unusable, or even unpleasant.
For compression-molded chips, the fact that the inlays are actually inlaid - i.e. compressed into the surface of plastic so that the inlay and chip are a seamless whole - matters a lot to me, which is bad news for me. It means that my tolerance for milled-and-relabeled chips is pretty low, which greatly limits the scope of possible customized chips I can get.
And finally, provenance matters to me. I like to know that there's something about the chips that makes them special, even if they're only special in my own eyes. That they aren't just objects, but rather objects that mean something, objects with an interesting story I could tell about them.