Master Nerf,
(I'm glad you answered the question, you'd be surprised at how many posters don't)
The Eotech 552 is supposed to be excellent for shorter range work. I don't know which Aimpoint is best, hopefully someone from the Sandbox can chime in on that one. But if you got the cash you can do a combo! (You'd be looking at an A3 model but I think you know that)
I wasn't going to say anything about the heavy barrel, but I agree with Steve. I think that esp. on the 20" the HBAR ruins the feel and handiness of the weapon. I can't really speak for the 16" HBAR but my Bushmistress M4gery sure is a handy little carbine. I prefer the 20" GI w/ A2 stock myself.
There's other bench ranger accessories like lasers, sure-fire flashlights, pointless front grip add-ons, etc. It's not a bad idea to get the Picatinny rail front handguards so you can add that "tactical" stuff but I'd get ones that also have covers so that the handguard has a rounded profile where there's not an accessory. Easier to handle.
Something with a bayonet lug will allow you to thrust a bayonet into their brains, something to think about when your mag goes dry.
And if you're from the south, save a little money to buy a Confederate battle flag. Fly it when they come for you....