Based on your description, you want a quality upper marked "5.56mm", since the civilian ".223" does not have to meet the higher standards of "5.56" in terms of barrel life, strength, etc.
While the lower carries the serial number, the upper is the key element as far as overall performance goes. Go with quality manufacturers, even for "just the upper". There are too many "Grade B" forgings around that need a lot of later handwork to get them into a respectable, in-spec shape. The better manufacturers machine their own, or their QC goes through more steps to make sure even the "trivial" specs are right on.
I don't know if you're looking for a "beater" (always good to have one of those, especially for learning AR15 gunsmithing on), or a "forever" rifle. In any case, get as heavy a barrel as you can handle, especially underneath the handguards, where GI standards, and weight savings, tend to thin out the barrel before it gets "fat" again. DO NOT buy a fluted barrel, because only the extra-premium ones will have a second heat-treating after fluting. The manufacturing world is only now starting to realize that machining itself can add potential stressed in unexpected places that come back and bite you thousands of hours, or rounds, later.
Consider a monolithic upper, with the forward rail section machined from the same piece of aluminum as the "real" part of the upper. Stay away from free-float tubular handguards. The one I got proved to be the biggest ass-pain of any AR15 work I ever did. The final results are great, but only after a lot of grief, and a good chunk of change for a carbon-fiber tubular handguard. No matter what you have, things start to get hot after the first few hundred rounds. Anything touching the barrel will get hot, including the gas block/gas piston, gas tube, rear handguard ring, and even the part of the upper that the barrel screws into.
A bit of trivia, but in a special test on a suspect lot of ammo, the Army discovered that the stainless steel gas tube melts into red-glowing linguine after about 950 rounds of really sustained full-auto torture firing far beyond anybody's specs. However, once the weapon was cool enough to touch, the gas tube was replaced, and it still passed the "serviceable for combat" standards. Just don't do it to your own weapon, ask a friend to borrow his. :)
A rule of thumb is to be prepared to spend $1K or a bit more for that quality upper. I'm already seeing guys coming back to the MSR store offering to sell back their $700 generics, only to be told that they can get $600 for the entire weapon. As the store owner tells them, "first, you didn't buy this from me, because I've never sold this brand. Second, an unfired weapon is still a used weapon once you go out the door with it, so $600 is the best you can expect". If I was shopping for an upper today in 5.56mm, I'd consider this heavy barrel, mil-spec upper from a company like Daniel Defense.
Slap on sights, and I'd consider it "ready to rock", although I'd tweak it a bit with a better flash hider than the GI type. Certain premium brands can both cut down muzzle rise, and dampen muzzle flash at night to just a faint puff of gas that's just about impossible to see beyond a few feet away. I'd also add insulated rail covers, and more rails, where needed. Anything metallic can get warm after 30 rounds of "quick" fire, and heat shields will stop shielding when saturated. The really good thing about my carbon fiber handguard was the composite started to get warm where it touched the aluminum rear cap, but stayed cool about an inch forward of that.
Here's the writeup at Daniel Defense upper.
There's a lot of detail on this one item, along with a good discussion of the mil-spec features you want on your upper, in general. Both Midway and Brownells have "build your own AR-15 configurators" that let you browse through their wares and give you a bill of materials. Just take basic "lower" choices, and concentrate on how your upper should look.