Get the cheapest, Mil-Spec lower possible with the best upper (emphasis on the barrel and bolt/carrier group). Save something in your budget for either good iron sights and/or a competent optic. You do not need an optic right away, though it's much better shooting experience with a good one. Practically speaking, a Ballistic Advantage barrel (which many companies typically will rebrand) will be good enough for most cases. Bonus points if you can get the Hanson profile "performance" barrels. Daniel Defense as of late has been having deep sales on their uppers, and their barrels are excellent.
Another consideration: use good ammo. Many of the problems people come across in terms of accuracy / performance are remedied with good ammo choices. However, most people want the cheapest ammo available which, while serviceable, is not the way you should test your rifle. The true cost of evaluating the performance of your AR-15 is more like .80 - $1.00 CPR versus .45-.50 that you see in range ammo choices.
The caveat to all of this: Anderson Rifles that come direct from the manufacturer or distributor will work very well. Same with PSA. Diamondback. These are $500-$700 rifles that are great platforms to build on or learn from if that's all you can afford. The (functioning) AR-15 you have is better than the one you don't.