My tastes are out of your price range. But as Robocop said, who ever told you not to go under 18" is an idiot talking out his ass. 16"= 6-800 if you can do your part.
My suggestion, spend money on a great trigger and barrel. Get a matched upper and lower set of receivers (same brand, at least, matched is better) everything else is up to you.
There are plenty of build threads here for you to look through as well as complete rifles for ideas.
I don't have time to build you a rifle though. If your going to build, you do the leg work.