Since you're going to pound the sod poodles you might consider getting a Harris bipod and a rear bag (a rabbit-ear bag is a good idea) of some sort to start off with. You might not get quite as good groups with the bipod, but it beats a rolled up coat!
A benchrest can run from the sublime to the ridiculous with regard to price and quality. You could start with a cheapie like that MTM triangle shaped job for around $50 from WSS, about or go whole hog with something like the JJ Industries Ultra Front Rest for $879 from Sinclair International. Generally a heavier rest will be more stable than a light one. I use a rest from Sinclair (they're the bigwigs when it comes to supplies for the BR crowd) that isn't offered anymore (apparently - I can't find it on the site) but is pretty similar to their Gen II All Purpose rest (except it hasn't got the quick adjust levers). That rest runs about $300 but it is about the best one I've ever seen. Heavy, either spike feet to prevent sliding on wood benches or rubber coasters for concrete. Adjusts easily and locks into place solidly. Maybe it's excessive, but it works for me.
....we all know Remingtons need to be trued up, have a new barrel installed in a new McMillan stock and a Jewell trigger installed to shoot like that
