Ok, my turn.
Some people get bent when you use the term sniper rifle. It's because we are not snipers. I personally don't give a s**t.
Budget Precision Shooting 101
.223 is the most bang for the buck, pun intended.
Remington 700 Tactical, 20" barrel 1/9 twist >$700
Bushnell 3200 3.5-15x40 >$450
bipod, cleaning supplies, carry case , etc... >$200
Find a deal on 500 rounds of .223 and save the brass
Go shooting
Put a target up at 100yd and learn how to hit it precisely. Move to 200yd and start over, etc...
When you've acquired some brass, start shopping for a press. Learn to reload and get good at it.
Once you know how to reload, you're ready to upgrade the gun.
After all this is done, you'll be on your way to precision shooting.
The most important thing to remember is, a precision shooter with a beat up gun will outshoot a beginner shooter with $10,000 worth of gear.
Get it?
Gun and scope choices are examples only....