HB anvils are some of the best you could ask for. Considering the quality, all you really need to do is knock of the loose rust with a wire brush. If you want, you can rub down the sides with an oily rag to prevent further corrosion and allow the natural patina to develop. The face will get plenty of abrasion when you're forging the hot steel, so there's no need to do anything special to it.
One tip, though, the Hay Budden anvils are a wrought iron body with a tool steel face plate welded to it. This means that it will wring like a church bell.... and that's annoying, to say the least. I've tried chains and magnets like folks recommend, but nothing has come close to the sound-deadening properties of silicone caulk or masonry adhesive. You can deaden the noise a good bit by placing a heavy magnet under the horn and heel (the places that resonate the most), but I've had far better quieting by squeezing half a tube of caulk or adhesive out on the stump before setting the anvil down. The firm joint this creates between the two pieces does a far better job of deadening than anything I've found.
