OK, here's what you want to know.
16" will have less velocity than 20". M193 does 3250fps out of a 20", it will do about 3100fps out of a 16".
When you get a 16" do NOT get an Hbar. Go for the light profile. This is often called a "pencil" barrel, or a "superlight". It is actually the original thickness of the A1 rifles from the Vietnam ear.
The one member above who told you about Colt pins is only half right. Older Colt's (green label) have the incompatible larger front take down pin. All new Colt's have the standard pin like any other AR manufacturer. Green label Colt's are much more rare and usually cost a lot, so it is almost a non-issue. Even if you got the older large pin Colt, they have adapter pins for cheap.
Model 1 Sales is not that good of a parts provider. However, their uppers are pretty decent. Their barrels are made by ER Shaw, and their uppers are forged by Cerro (same place that does Colt, and a number of others). So the components making up their uppers are pretty close to just about anything else out there. It is their lower parts and bolt/carriers that are severly lacking in quality.
Model 1 Sales offers a lightweight barreled upper in either A2 or A3.
Bushmaster offers the same in A2 or A3.
Colt has a lightweight upper, but it will be well over $500.
JT Distributing offers a good quality light weight upper in A2 or A3 (they are also a kit seller like M1S) JT Distributing is the kit business side of DSA arms, who makes a decent AR.
Bushmaster is by default chrome lined in the chamber and bore. M1S, JT will have it as an option. All will be 1/9 twists.
As for the Bolt carrier group. If you are going to shoot this upper a lot, then yes - you should get a seperate bolt and carrier w/ charging handle for the lightweight upper. This is so they "wear together". Headspace is not an issue on bolts or barrels that aren't shot much. However, some people say that it may become an issue when using a well worn bolt and a new rifle, or swapping well used parts.
The M1S and JT upper can be had with chrome lining and boltcarrier + charging handle for less than $500 easily. The Bushmaster is $405 less bolt and carrier and charging handle. Figure $150 for those ($130 for BCG, and $20 for CH)
I'd get a Colt, but since your budget is $500, I'd try and stretch that to a Bushmaster with bolt and carrier for $535. Note that Bushmaster has a huge backlog and will take a while to get your order out. Call before hand.