Re: Remington 700 SPS Varmit 243
I say go for it... out of the box, it can be a coyote killing machine. You (probably) won't be getting the same accuracy as your old VLS, but that SPS can be an excellent hunting rifle, and as you want more accuracy from it, this is a very easy platform to start with.
A good stock is probably one of the main reasons your VLS was "a tack driver" The cheap plastic stock that the SPS comes with is it's main drawback, buts an owner of 2 Remington 700s with sporter barrels, there are probably more aftermarket stocks available for the SPS Varmint than most other guns. Ditch the stock for an aftermarket one, have the action gone through and the trigger tuned and you'll see the accuracy improve. The .243 is perfect (for me) for coyotes as well.
As far as scopes. You won't NEED that much scope for coyotes on that rifle, but it may help later on as you start doing other things with it. All in all that is a great place to start (providing you don't overpay) - but keep in mind there are some pretty good choices for you in that price range from other brands like Savage, Browning, Howa, Weatherby Vanguard etc