If you move to Norfolk and you want your children to play sport at a good level I'd stay localish to Norwich. The sports facilities in the rest of the county (for higher level atheletes) aren't amazing and you'd have to travel to Norwich anyway. The UEA has great sporting facilities that lots of clubs use.
If you live very rurally you can be cut off by the snow during bad storms in the winter and the Internet and mobile connection is still iffy in some places.
If you are likely to need regular access to hospitals there are three in the county, Queen Elizabeth in King's Lynn, Norfolk and Norwich in Norwich and the James Paget in Gorleston.
I don't know much about Kings Lynn but Gorleston is a residential town right on the coast between Lowestoft and Great Yarmouth, it does not have the social problems and isn't rundown like either of the other two bigger towns. My parents moved there from London 20 years ago its a nice place to live, not far from Norwich (35 mins), walking distance to a large sandy beach. It isn't quaint like Southwold and older Norfolk villages but £600k would get you a lot for your money in Gorleston or the surrounding villages like Fritton, Belton, Bradwell, Haddiscoe and up to Beccles.
Beccles is a smaller quainter village slightly more inland but with a strong sporting centre, good rugby, foot ball and cricket teams as well as Brownie, scout and cadet groups, it also has a lovely lido and river for canoe and kayaking etc.
Schools in Norfolk are all comprehensive there are no grammar schools although there are a few private school