Kenneth, this will fit the bill quite nicely. You will get a rifle that has excellent cost to function value and the kicker is the legendary Savage "Out of the Box" accuracy. I have several Savage rifles and they don't disappoint.

here is a review on the Mossberg MVP predator I linked to "The MVP is a keeper. Why? Three reasons. One, it's accurate. Two, it takes AR mags. Three, it's economical." americanrifleman.org/articles/2012/9/10/the-mossberg-mvp-predator/

Rick C what problems have you had with the Mossberg MPV rifles I have found them to be will made and more accurate than I will ever be

Kenneth - Depends on the size of your varmints. You might well be perfectly good with a simple bolt action 22LR. If you're talking coyotes, or similar sized varmints, then you'll need a .223, 25-06, or 243 maybe .. something along those lines. Savage does make some decent, less expensive rifles, so you're looking in the right direction. My only advice for certain is to avoid Mossbergs. Stick with Savage.

You did not say which th xp model or caliber but check out this Mossberg .223 varmint gun it is also a excellent choice budsgunshop.com/catalog/product_info.php/products_id/79796/mossberg+mvp+var+18+hb+223+lam+11rd