The "Varmit Rifle" is actually the .223 Bolt Action Rifle. I would recommend doing this after you've completed all the pro hunts as quickly as possible as there is a 10x credit bonus for any game you hunt.
Once you have done this you can buy up all the parts for the gun which include ammo and scopes unique the rifle.
Of course you should do all the missions first (if you're going for the complete) before grinding out on free roams.