If you do decide to rebarrel this rifle, I strongly advise that you lap the locking lugs. It is not hard, takes about 15-30 minutes, and should produce a noticeable decrease in group size. The bad thing is that this will make the rifle have excess headspace, so it needs to be done in conjunction with a rebarreling job, not by itself. A lapping kit should be available inexpensively from Brownells, or ??, and can be used for many rifles.
A replacement trigger is something to consider, for bench-rest level accuracy.
What barrel you go with is going to depend on the contents of your wallet, and your desired level of accuracy. To start with, though (and this is not a recommendation, just a starting price range), a E.R. Shaw barrel in stainless is going to set you back (I think) about $250, and then the fitting will be on top of that. Prices go up from there.
I personally like E.R. Shaw barrels, and think that a 788 with a Shaw barrel should be more than adequate for varmint hunting, although perhaps not for competition. Good luck.