I've built several AR's on Anderson lower receivers, and they all work just fine. A couple of them had the out of spec buffer retainer pocket which was annoying, but an easy fix. I'm sure they have that issue worked out by now.
As far as parts kits go, I'd skip the Anderson parts kit and check out Palmetto State Armory. They usually have decent prices on lower parts kits and lower build kits. Most importantly, you can get parts kits that don't include the trigger group, so you can go with a good one right from the start. Trust me - even if its a budget build, a good trigger group will save you a lot of frustration and make your finished product a lot more fun to shoot.
Regarding the .223 Wylde - in theory, it should be inherently more accurate than the 5.56 chamber. In practice, It's not likely going to be a noticeable difference, unless you plan on getting serious about squeezing as much accuracy out of your rifle as possible. In short, that's not something I'd get too concerned about on a budget build.