Well Fringe, you've had masses of good advice! The 'twee' bits of Norfolk and Suffolk can indeed be pricey, but other bits less so, you can scan Zoopla, Onthemarket, etc to get some likely comparisons of what your sort of property might cost.
We liked Norwich, but some of the surrounding villages will differ in price. We've stayed in Holt and Wells (close to GSM perhaps) and they're great, but only you know your budget?! We also stayed in Hunstanton (we liked) and visited King's Lynn (which gets criticised - though we thought it was OK - and I believe has parts prone to floods). In Suffolk, Bury and Stowmarket looked fine to us, and Ipswich too, but we weren't looking for hospitals, GPs or dentists!!!
Up in Lincs, usually described as one of the cheapest counties, we've stayed in Horncastle and Louth, both very nice (especially the latter, a terrific market), but as you've been warned, some of the southern end has flooding issues, and I recall forums when the 'locals' slagged off what the likes of Wisbech and Boston have become, as they felt they were being marginalised in their own country? I recall an old friend, who's now up in I think Brigg, giving that a good word, also the likes of Market Rasen and Woodhall Spa (further south).
Perhaps surprisingly, she also gave a good word for Cleethorpes, which has reasonable trains into South Yorks and across to Manchester & Liverpool. Someone else I know gives good reports of Peterborough (actually Cambs) which has a fast train to London if needed, and decent facilities, a reasonable ride into Norfolk if needed?
Jolly good luck!