Liverpool to WR is a long day. You could break overnight in Brussels or Liege, which may actually work out cheaper, and get there early afternoon, or go via Hoek and arrive late afternoon.
If you are really after a bargain and don't mind a couple of hours extra on trains, use Dutchflyer as far as the German border at Werner and a Niedersachsenticket from there via Bremen to Vienenburg. Pay the last bit to WR separately.
Might be worth considering Halberstadt as a base (and riding its trams) but you may have accommodation arranged via HSB.
If you end up flying, which of course I cannot advocate (especially as I'm about to fly home from Prague ☺), LIV - Berlin with Easyjet might be worth it, as you can get to WR reasonably easy on regional trains. The alternative is Flybe MAN - Hannover but it currently gives an inconveniently late arrival in Germany. Hamburg isn't out of the question either, in which case visit Miniaturwunderland there.