After much debate and looking about I needed a gun that was pretty inexpensive to shoot and was the best "bang for the buck". After looking at guns in the $500+ price range and knowing my wife would kick my rear, I decided on a compromise gun.
It is a H &R Single Shot .223. It has the Varmint "Bull" Barrel and came with a 3 x 12 scope, picatinny rails, etc. It has no open sights at all. I've only put five rounds through it so far and the one thing I noticed quickly is IT IS LOUD!
What I do like about it is it has enough weight for me to hold it steady. What I don't like is my big thumbs trying to get to the hammer under the scope. Anyway, this is the first centerfire rifle I've ever owned. It should be just fine for Coyotes, Groundhogs, and Prairie Dogs.