If i were in your shoes, I'd do this
Faxon 16'' Pencil Barrel - $180 shipped - http://www.aimsurplus.com/product.aspx?item=XFXB16PM&name=FAXON+FIREARMS+16+IN.+Pencil+.223%2f5.56+4150+QPQ+Nitride+Barrel&groupid=6477
AIM Nitrided BCG - $90 shipped - http://www.aimsurplus.com/product.aspx?item=XAIMBCGN3BDG&name=AIM+AR%2fM16+.223%2f5.56+Nitride+9310+MPI+Bolt+Carrier+Group&groupid=723
TRS-25 - can be found for sub-$60 on Amazon Warehouse deals if you keep an eye out.
OR
Ballistic Advantage 16in, mid-length - $130 -http://www.primaryarms.com/ballistic-advantage-ar-15-556-nato-16-mid-length-barrel-12x28/p/babl556015m/
AIM Nitrided BCG - $90 shipped - http://www.aimsurplus.com/product.aspx?item=XAIMBCGN3BDG&name=AIM+AR%2fM16+.223%2f5.56+Nitride+9310+MPI+Bolt+Carrier+Group&groupid=723
Primary Arms Micro-Dot w/ Full Co-witness Riser - $120
Either one could bust your budget by 10 or 15 bucks (RDS price on option one, shipping on option 2). You're bascially choosing between a little better barrel on the first choice, and a little better RDS on the second. I'd go with the better barrel. I've run several TRS 25s, and for the shooting you're describing they'll work fine. No prob with the folks suggesting PSA for a BCG, but i like AIM's fast (and free) shipping so they're my preference over PSA.