There are many common lengths. However, the most common are the 16" and the 20." Of the others, 14.5" (with pinned muzzle device to bring overall barrel length to 16" to meet ATF requirements) and 18" are the next most common.
Simply put, a 20" barrel gives more velocity, but also weighs more. Velocity cannot be understated. Especially with a round in the 5.56 mm that depends on high velocity for maximum effectiveness.
16" barrels are lighter than the 20" counterparts, but also produce reduced velocity. Since most uses of a Patriot rifle would take place inside of 200 yards, the difference is minute.
Heavy barrel, pencil barrel, and government profile barrels are the most common. Of the heavy barrels, one can get the barrel fluted, which reduces weight without sacrificing much of the barrel's stiffness (and, therefore, accuracy).
Government profile is OK in a 20" barrel. For the 16" barrel, the heavy profile is a much better choice.
Chrome lining resists wear due to heat when shooting many rounds in a row ("mag dumps").
Stainless steel and Chrome-moly (aka "unlined") barrels are more accurate.
I would choose either a stainless steel heavy barrel in 16" or a chrome-moly government profile barrel in the 20"
Basically, there is the flat-top, and the carry handle. If you go with the carry handle, there are "A2" and "A1" variations.
I suggest a flat top. You can always add the removable carry handle.
There are many variations in stocks, but the two broad variants are fixed and adjustable. Adjustable are clearly more versatile. However, if you have really long arms, then a fixed stock would be fine. Similarly, if you have shorter arms, and never extend a collapsible stock, then a fixed carbine length stock ("shorty") might be just fine for you.
Fixed stocks are good for 20" rifles. That said, the Canadian "A7" look (20" barrel, collapsible stock) is pretty useful. Some people use a fixed stock on a carbine. That is OK, too.
Collapsible stocks offer the versatility for most people.
There are many types of handguards on the market. Regular handguards are just fine. There are many aftermarket drop-ins that are equally suitable. I like the Magpul handguards. Some handguards are free-floated - greatly assisting in accuracy.
Of all the types, I suggest a free floated handguard. LaRue and Daniel Defense make a lightweight, easy-to-install variation that is not too thick to hold. I also suggest the rifle length handguard, though midlength and carbine length are acceptable for specific needs / wants.
Of drop-in quad rails, I suggest KAC. They are lightweight and slim enough to handle well. They are neither cheap nor really easy to install, but they are worth the extra money and effort because of weight and thickness.
I suggest a LaRue or DD 12" free float quad rail.
Get a trigger upgrade. Geissele and Rock River Arms make good, relatively inexpensive drop-in replacements.
1st choice - ACOG.
It offers magnification for rudimentary scouting / reconnaissance. It offers a Ballistic Drop Compensator (BDC). This not only helps you to know where the bullet will strike at a given distance, but also to measure that distance, too. An ACOG is rock-solid, and can even be used as a red dot, utilizing the Bindon Aiming Concept (BAC). In a pinch, the ACOG can be used as a hammer.
2nd choice - Red Dot
The red dot is the fastest optic available for close quarters action. When zeroed at 50/200, the red dot can be used effectively out to 300 yards (one dot hold over). Red dots are generally used with both eyes open.
3rd Choice - Multiple power scope
Some call these hunting scopes. Can be used successfully on an AR15, however, this is not the most useful for the American Patriot in defense of liberty. Still, scopes are better than irons for many people, so it is a valid option.
4th Choice - Irons
To be sure, Iron sights are needed for backup with all optics. For fixed sights, I suggest a 50/200 zero.
On the whole, I suggest either a "RECCE" (sounds like "Becky") build or an M16A4. Second-tier, but very useful builds include:
- M4 series (will be range-limited and accuracy is the worst of the bunch)
- M16A2 / A1 (length and weight are a concern, as are the fixed iron sights)
- MK12 Mod 0 / SPR (again, length and weight are a main concern)