The quickest cross-country route (but only by a few minutes) is usually to change at Peterborough and then again at either York or Leeds. (The connecting point varies depending upon when you're travelling).
But it's simpler to go direct to Manchester Piccadilly and catch a direct connection to Blackpool from there. It only takes 5 or 10 minutes longer. (It's a bit over 6 hours on either route).
Going via London and Preston is usually slightly quicker (with typical journey times of between 5½ and 6 hours) but it could be much dearer. The off-peak fare on the cross-country route is currently £112.00. There's no return fare available via London; you have to buy two singles. If you paid the off-peak 'walk up' fares at the ticket office you'd pay a total of £241.60 (at current fares) but there are some cheaper advance fares available on that route. (I can't quote a figure because nearly every train has a different fare for the journey). Advance fares aren't offered on the cross-country route.
The National Rail website only goes 3 months ahead, so you can't check the exact details of your journey (or search for cheap advance fares) yet. But, by entering some dates in, say, March you can get a rough idea of what will be on offer later in the year:
http://www.nationalrail.co.uk/
(If you just enter 'Norwich' and 'Blackpool' as your start and finish points you'll only be offered cross-country journeys. Click on 'Advanced search' to add 'via London').
Chris