It is a simple matter to build an AR when using an assembled upper.
I saw a Colt M16A1 GI surplus upper cheap ($175, excellent, like new), and, since I wanted a retro clone rifle similar to the M16A1 I fired at Camp Perry circa 1980 at the Small Arms Firing School, I bought it. The days of cheap surplus A1 uppers is largely over, though.
Putting together the lower was easy...I used a Double Star lower, and my rifle has functioned perfectly.
Since then, I found a used "post ban" A1 (actually "C7") shorty upper, 16" Hbar without flash hider cheap on the equipment exchange at AR15.com. I paid $150 shipped, and it is in excellent condition.
I bought a collapable CAR-type stock for it, but my favorite set-up is to have the A1 buttstock and the shorty upper...makes for a short handy carbine with a solid stock.
I like to keep my AR simple...no rails, A1 sights...just an accurate, reliable rifle. When I am at my rifle club, there are often several AR's being shot...tricked out rail equipped, lights, holo-sights. I have often out-shot them with my old-fashioned M16A1 clone, either with iron sights or a Hakko 4X AR scope on the carry handle...that, and it is 100% reliable, unlike some of the other AR's I have seen.
I am still using just the one lower, switching uppers and stocks as I see fit...since both uppers have their own bolt carrier and bolt, I have two thirds of a second AR...I will probably pick up a second lower and make a complete second rifle one of these days.
BTW, DSA has a very good deal on flat-top M4-style uppers going on...there is a wait to get one, but they get very good reviews.
My main advice is to get the best upper and bolt carrier group you can afford.