I would buy a LMT SOPMOD lower with the match trigger and attach a pre-built upper of your choosing. It will be cheaper than buying it outright and you'll get exactly what you want. The LMT lower assembly is usually in stock at Rainer Arms for around $550.00. Buy a premium upper with a quality barrel and free float tube.
You will have well over $100 to $150 for tools to build it yourself unless you already own a torque wrench. You'll need a large vise and float tube and barrel nut specific wrenches. I have built dozens of rifles, but would not recommend a new person doing it on their very first AR-15.
You could just buy a new Colt, LMT or Daniel Defense rifle and run the crap out of it. When the barrel stops shooting accurately (6,000 to 10,000 rounds) simply rebuild it if you like.