I am Currently seeking a rifle on a low budget. I want an accurate single shot for varmit hunting. That is cheap to shoot. Any Brands or Caliber suggestions?

The NEF handi rifle in 223, or the H&R also in 223. They are as low priced as you can go and still get some ammount of quality. The 223 caliber is the lowest priced ammo available in center fire, when using Mill spec, bulk packed ammo you can shoot cheeper than reloading! I would also suggest you look at a Stevens bolt action repeater, maybe no more money and likely better accuracy, also in 223.

I'll second the .223. You can get a Black Hills box of 50 very reasonably, and they shoot fantastic in most rifles.

And an H&R or NEF single shot would probably be your best bet.