So the only difference is that:
A2 has a handle,
A3 the handle can come off,
A4 does not have a carry handle?
I can help you with this a little bit.
The "A2" rifle has iron sights that aren't removable. Their easier to adjust then on the older "A1" rifle. The "A2" also has a 1 in 7 or 1 in 9 inch twist depending on the manufacture. I think the "military" uses the 1 in 7 twist. The 1 in 7 and 1 in 9 twist work better "in most cases" with the heavier "SS109" 62 gr. bullets. The U.S. military calls them "M855 Ball" The older "A1" had a 1 in 12 inch twist. They worked good with the U.S. M193 55 gr. bullets.
The "A4" is the same rifle as the "A2" but without sights. They come with a Weaver style scope mount. Other then that they are the same rifle.
I'm not familiar with the "A3", but you might be right as far as the handle coming off.
I bought a new Rock River Arms AR 15/A2 Tasc Rifle last fall. It has a 16 inch barrel with the 1 in 9 twist. I got to tell you, this rifle is unbelievable. I was shooting it yesterday using "SS109" ammo and was shooting around 1 inch groups at 50 yards with the factory sights. I started to shoot at 100 yards but had a "shell case" break and I had to go home and remove it. It broke on the side, the rim I guess where the ejector grabs it.
The guy that got the rifle for me has a Rock River Arms AR 15 Varmint rifle with the EOP (elevated optic platform) a 24 inch heavy barrel and his has a 1 in 12 inch twist for use with lighter bullets 40 to 55 gr. His shoots 5 shot 3/8 inch groups at 100 yards. Thats a little better then my remington model 700 223.
If your looking for a rifle to have fun with and thats cheap to shoot, the AR 15 might be just what your looking for. I would look at Rock River Arm's, Olympic Arms or DPMS. They make high quality rifles at a lot better price then say Bushmaster or Colt. My good friend has a Colt and a Bushmaster and I don't think their any better then my RRA.
Hopefully when/if the "assault weapon's ban" end these guys that are hanging on to their "preban" AR 15's that think their worth their weight in gold come back to reality. $1000 or $1200 for an basic AR 15/A2 (used at that) you got to be out of your mind, in my opinion.