Re: Looking for ideas on a good first AR
Get a BCM. I suppose tactical feel means you don't want a 20", although that would be good for hunting bullet ballistics. If you are truly close enough to make good shots on deer, I assume you are using good 68+ gr ammo, and short range. With practice, you should be able to do this with the small aperture on the Larue BUIS which will add $90.
BCM may still have uppers on sale for $50 off, so you'll need the barreled upper ($375), bolt carrier group and charging handle ($135), a p-mag ($15), and a complete lower (maybe $300). Figure a dollar a round for good ammo, I think Winchester Silvertips get good reviews.
With the remaining cash, you may be able to get a decent red dot. I don't think you're budgeted for a rail, tho.