If you don't want to buld one (which is a ton of fun); I'd go with a Daniel Defense mid length rifle. Larue also makes a really nice rifle. Those would leave you with plenty of money to buy a nice optic (around $500 for a non magnified aimpoint / eotech, or $1,000 for a magnified optic).
I'd go with a mid length gas system if you're getting a 16in barrel (standard). Carbine gas systems just look goofy with that barrel length.