I think that unless you're going for a high-precision match gun, a 5.56 chamber gives you better options. My AR has a 16" mid-length heavy Rock River barrel in 5.56, and it is more accurate than I could hope to be.
I personally sight my rifle in at 50/200m (they're essentially the same in the AR platform at 5.56 velocities) using 5.56 ammo. I reload, so my plinking load is a moderate .223-spec load using VV135 worked up for accuracy, running at around 2740fps. This is my most accurate load, and I got a 7/16" group at 50m with the 5 rounds used during my reload workup. POI is a little lower than with the Q3131A1 round, around 1 MOA at 50m. The advantage in this situation of zeroing with the 5.56 ammo at 50/200m is that when switching over to the lower-velocity .223 plinking rounds, POI is fairly close to target center (2 or 3 inches or so high versus the 4-5 with the 5.56) at 100m. A 50/200m zero will put rounds about 4.5 MOA high on the target at 100m using 5.56 velocities, but if you're using lower velocity ammo, POI drops along the line, wth the trajectory drop being more severe the further you go out.
In my experience, factory .223 from most manufacturers tends to run on the hot side, so you're practically only going to see around 250fps or so difference between 5.56 ammo (Winchester Q3131A1 clocks around 3200fps in my gun, vs around 2950 -if i recall correctly - for something like the Monarch 55gr). This means there will be less difference in POI between 5.56 and .223 ammo then with my plinking reloads, but still some, nonetheless.
This can be adjusted for on my red dot by adjusting a few clicks to move POI in line with the 5.56 ammo. How and what ammo you zero with really depends on what you're going to be shooting. You can always re-zero later, if you change your mind.
Also, since we're talking brands and models of ammo here, I've found that the Winchester Q3131A1 5.56 NATO ammo to be very good in consistency and accuracy. It is the most accurate commercial ammo I've put through my rifle. From what I understand, this is the standard IDF 5.56 NATO load. As mentioned, Academy doesn't carry it or any other 5.56 NATO ammo, but you can find it readily at Cabela's and other similar stores. Cabela's puts it on sale pretty frequently at $8.99/box. I've got a few hundred rounds of it built up in my stock. If you ever get out near Brenham, Ammunition To Go carries this stuff at a decent price. It comes out to $9.08/box when bought in quantities of 500 rounds, or $9.19 in quantities of 100 rounds:
http://www.ammunitiontogo.com/product_i ... 6-fmj-ammo
http://www.ammunitiontogo.com/product_i ... 6-fmj-ammo
For .223 ammo, I've found that PMC Bronze performs quite well. It's not quite as good as the Q3131A1, but it is also considerably cheaper. I believe Cabela's has it on sale for $6.49/box right now. I went and bought 600 rounds of it the other day:
http://www.cabelas.com/product/Shooting ... 731863.uts
I made a comparison of several different commercial loads off my lead sled, if you're interested in looking at those. Keep in mind, this will vary with different barrels, but it's a good starting point if you want to take a look:
http://therealnecessities.blogspot.com/ ... tests.html
Pro Tip: Cabela's will honor their internet price if the store rings it up at something higher. I went to get the PMC ammo from them, and it rang up at $7.99/box. I pointed out that I'd scanned it at one of their little kiosks in the store and it came up there at $6.49. The cashier then overrode the price to match the price listed at the kiosk, and saved me $45 ($48.71 if you count tax savings as well) in the process. Alternatively, you can also buy it online and have it shipped for In-Store Pickup (no shipping cost). When it arrives at the store, go and pick it up there at the service desk without having to hassle with checkout.