I would suggest a few things.
First, I would try not to seek precision accuracy from a subsonic load at any significant distance. I have done the exercise, downloading .223 (7gr) and .22-250 (9gr) with Unique and the 52gr SMK. Shooting at 100yd, accuracy under absolutely still conditions wasn't even equal to the .22LR, and when the wind picked up, the targets looked like shotgun patterns. Subsonics and wind are not compatible. Fageddaboudit!
Get yourself a Dick's Sporting Goods special Savage 11VT .223
http://www.dickssportinggoods.com/shop/index.jsp?categoryId=12270519. Drop another $250 roughly for a Mueller 8-32x44 side focus target scope
http://www.amazon.com/Mueller-Target-Rifle-Scope-Black/dp/B004689ZWQ/ref=sr_1_2?ie=UTF8&qid=1441562569&sr=8-2&keywords=mueller+8-32+44+side+focus. Get into reloading and start load development with the 52gr Sierra Match King.
...and that's just scratching the surface with precision shooting. BR comp is another several levels beyond that.
I've been shooting F Class and other (non-BR) comp for a couple of decades, including several years of 1000yd F Class Open.
Your remind me precisely of myself back when i was getting started. I strongly encourage you to find a shooting club and listen hard when you get there. Ask at your local gun shop. Be prepared to pay your dues. You will love pretty much every second of it, but doing it on your own is the surest way to discouragement. We all need help.
I think your best, easiest start is to get a reliable 22LR bolt rifle, like the Savage MKII
http://www.gandermountain.com/modperl/product/details.cgi?pdesc=Savage-Mark-II-F-Rimfire-Rifle&i=416267, and an inexpensive scope like the Tasco 6-24x42 MilDot Varmint Target
http://www.amazon.com/Tasco-Target-Varmint-6-24x42mm-Reticle/dp/B000GEY6L4/ref=sr_1_1?ie=UTF8&qid=1441562020&sr=8-1&keywords=var624x42m (VAR624X42M), and some moderately priced good ammo, like CCI Standard Velocity Target. It's the rifle I used as an Instructor for years in NRA Youth Marksmanship training. It can get you as far as Rimfire Distinguished Expert, mine has served several young shooters in doing just that.
It may sound like a step backward, but this grade of equipment can develop all the skills you will need before you move up to heavy barrels, and handloading, and fractional MOA's at several hundred yards.
Greg Langelius.