Since there has been lots of good replys above leaning to either side of the age old 223 vs 22 Varminter issue, guess I'll take the middle road to give you something else to consider. The best of both worlds would be to go with a 22BR. That said...
I have several 223's (rifles and pistols), 222's and 221's (rifles and pistols), and have had several 22/250's (rifles and pistols), although I am down to a single Browning High Wall in that caliber right now... and some 22cal wildcats reside with me as well. Kind of tried most of them over the years I guess. Since you commented about going for everything from diggers up to coyotes AND want one gun to do it all while your get your feet wet... I'd bet 90-95% of your shooting could be handled just fine with a 223. If you don't reload and can only have one gun, my vote would also be to get a 223. Every hunter should have at least one of them.
Have heard lots of good things about the Savage's, and they are a fairly cheap way to get in for the first timer - well worth your checking into them. My tastes go to the Remington's, Browning's and Cooper's, and I am having very good luck with all of them.
Since you mentioned the 700VS... I have one in 223 with a 2 ounce comp trigger and Leupold LR scope that my digger hunting pards call The Black Death - for good reason. It takes very few prisoners (I call it The Modgitator). The 700VS 223's are tack drivers right out of the box (so where does "tacks" fall between diggers and coyotes?). :wink:
Whichever way you finally go, welcome to the world of P&V calling and hunting. BTW, kiss your wife and kids goodbye before you start... you won't be seeing much of them anymore. :lol:
Ladobe