Which measurements are most important to consider for tall men? I am 6'8" and 255lbs so my figure is a bit between Kevin Durant (not as skinny) and Lebron (in shape but not as muscly). For smaller bikes such as what you would find in Wal-mart, I frequently see bike weight limits of 200lbs or so despite me still being able to still ride the bikes without any noticeable issues other than my knees hitting the handlebars. I thought bigger wheels (27"+ or 650b) would help, but I still see this weight limit which is absurdly low IMO as I'm a pretty skinny guy.. I saw another bike that had a suggested limit of 300lbs, but the recommended height limit was 5'7-5'10. Then I found another bike which claimed to support up to 6'3 and 220lbs, but the bike frame was smaller than all of the others at 17" where the others were set at 18". 

Because I'm looking for bikes under $500 so that I can ride around my neighborhood, I'm going to have to compromise in some size aspect but am not quite sure which size aspect matters the least: bike frame size, recommended weight limit, or wheel size. I saw other questions about tall riders but nothing specifically addressing this aspect.
Among quality aka dealer-level bikes, each model comes in a range of sizes. Wheel size in and of itself is immaterial to fit. Published weight limits are not typically contingent on frame size, i.e. it's the same number for the whole size run.

There are questions on here about how to interpret weight limits, but most dealer-level bikes are somewhere around 300lbs, especially for more entry-level bikes.

All but the biggest bike companies wrestle with economies of scale for bikes on the far ends of the size bell curve, so that's usually the main place someone your height will need to look. In other words, you're likely looking at barely squeaking in, if that, on an XXL hybrid or MTB, and many companies only go up to XL. In the US, brands I know that do XXL on a lot of bikes are Trek, Specialized, and Cannondale.