"Anything better than a Wal-Mart knife" leaves a lot of room. I know a dude who makes knives (he's really a sharpener), where you can get a 10", wide chef's knife for 12 bucks that's probably better than most anything you'd likely buy at Wal-Mart. But then, what's "better" to you?
Sharpening is key. A crappy dull knife is on par with a stupidly expensive dull knife. And if your plan is to get somebody at a local Farmer's Market with a truck and belt grinder to sharpen your knives, then... chances are it's a really good plan if you want to spend $12 on a knife. If you want to spend $200 on a knife, you (in all likelihood) need a better sharpening plan.
- steel: kind of steel will go a ways to determining edge-taking and edge-holding properties. So this involves how sharp a knife will get, but also how easy it is to sharpen. If you're sharpening knives yourself, both of those things matter. (Geometry and heat treatment of the steel, matter here, too).
- profile: you may have no preference, but this is another factor when deciding. What's the shape of the knife? Does it suit your "action" (how much belly do you want, how much 'flat'?). How tall?
- Geometry, but I'll leave that for the "steel" section
- Fit and finish
- visual appeal
I think most of this doesn't matter to you, since anything better than what you find at Wal-Mart is going to be ok. What DOES matter a lot is your ability to sharpen, or willingness to learn to sharpen, or plan to get and keep a knife sharp. If you have that piece clarified, then you can clarify how important edge-retention is to you, too.
I'm spouting at random, here. There are more organized posts throughout this forum in helping someone "new" to the thought process. But the only next step I can think of is to throw out some names of the less expensive knives that more or less well-liked. And then that would take all kinds of caveats.
OK, I'll start. Forschner Fibrox (or Rosewood handle) chef's knives are good bang for the buck. Only consensus is that the profile sort of sucks on the chef's knives. And edge retention isn't great, but that's going to be par for the course if you want to spend not much, and it might not matter. Dexter-Russell, anything on clearance at C&M (with "NSF" on the side) will be really inexpensive, too.
If we want to talk about steps up, Fujiwara FKM, Tojiro, Mac Pro, Yoshihiro (we're moving along a price continuum pretty precipitously at this point).... when you start talking about $200 your options open up tremendously. Except it doesn't make sense to do that unless you want to spend MORE on sharpening. Or have someone really competent to do it for you.
I'm stuck on your "Wal-Mart" baseline. Even though I don't really know what's available at Wal-Mart. Before I ever posted here, I browsed through the history of posts a bit, and ran into what is still perhaps my favorite (maybe 2nd favorite -- not sure) quote about cutlery (courtesy BDL): "A knife is just a handle and a sharpening problem".