Wow... Wide variety of answers here, but I'm not sure if they address what you are looking for specifically. I'd HIGHLY recommend getting a full factory AR, but get it while keeping the items below in mind.
Here's the basics...
RECEIVERS:
Uppers and Lowers - There are two major parts to every AR rifle... The Upper and Lower receiver. The LOWER receiver is the part with a serial number and is technically the actual "gun" and needs to be bought through a gun dealer. It holds all the trigger and mag release components and the stock attaches to it. The UPPER is just the top half of the rifle, which includes the bolt, the barrel and the housing, called the "upper reciever." You can buy the entire upper through the mail if you wish, and have it delivered right to your front door. Generally speaking, AR uppers and lowers are 100% interchangable. Pop two pins and swap in less than 20 seconds.
A1, A2, A3 receivers: This refers to what kind of UPPER you have. The A1 was the original Vietnam-era type, you'll never see one so don't worry about it. The A2 has a permanently attached carry handle. The A3 has rails along the top of the rifle, so you can attach sights, scopes, even a carry handle if you wish. Get the A3.. It's just so much more flexible.
BARRELS:
Caliber: The 5.56 can shoot a .223, but a .223 CANNOT shoot a 5.56. Remember that. The standard AR can fire a variety of calibers simply by swapping out the UPPER. You can have a 5.56 NATO, 9mm, .22LR, 6.8SPC upper and attach it to your LOWER without changing a thing. The mags may be different, but that's it.
HBAR?: As you just learned, it's part of the UPPER. There are many options... Bull, HBAR, M4, etc etc. Bull barrels are easy to spot... About 1" in diamter the entire length. HBAR's are Heavy Barrels. M4 is just the M4 profile barrel. The heavier barrels are good for dissipating heat during heavy sustained fire, but unless you are going full auto (which you won't) they do little else other than make the barrel heavier. As a previous poster mentioned, 1 in 9 twist is pretty standard.
Length: How long do you want your barrel? To be legal, it must be a minimum of 16" long. The shorter the barrel, the lighter it will be, but the bullet won't be as fast so it will drop faster making longer distance shots (200 yards+) more difficult. Standard lengths are 16, 20, 24".
Chrome or not to chrome: Barrels come in 3 types... Chrome-lined, Chrome-moly and Stainless. Chrome LINED barrels last longer than Chrome Moly, but only after about 20,000 rounds. They are easier to clean and more expensive, but are not as accurate as a Chrome-Moly. We're talking fractions of an inch in terms of accuracy, so unless you're a competitive shooter you'll never know the difference. Stainless is very durable as well and easy to clean, but also expensive. The same applies to the bolt carrier group (BCG). The chrome is harder material, easier to clean and wears better, but only if you're doing 10,000+ rounds of shooting.
Generally speaking, MOST AR manufacturers are quailty and mil-spec. Some are not... Hesse is one to avoid and I've heard sketchy things about Olympic. Model 1 Sales (M1S) are parts kits that people assemble. Some quality ones in no particular order include Bushmaster, Stag, Colt, DPMS, Rock River, Spikes, DoubleStar, Noveske, LMT... too many to list. A simple Google search will help you there.
Last things... Don't pay any more than $1200 for most brands, and that's on the HIGH end. You can get a nice set up for about $900 now. The major parts I listed above are the parts of the gun that you buy once and will not likely to replace anytime soon. Everything else can easily be replaced at home by you. You can swap out flash suppressors, handguards, stocks, grips and sights very very easily. As you become more familiar with your rifle, you'll discover new ways to customize it to your needs. Have fun and good luck.
Here are a couple different AR styles...
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=182950513
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=182350457
http://www.gunbroker.com/Auction/ViewItem.aspx?Item=182995846