The east coast can be very cold but it is drier too.
I agree with the posters who say think carefully about moving to somewhere small and with few - and, in my experience - ever dwindling amenities. Shops, post offices, pubs and buses are disappearing at an alarming rate in very rural areas. Where my Mum lives (Suffolk), the buses aren't too bad - every hour or so, but stop at 6pm, none on Sunday, and the largest shop has closed, leaving only a very small shop with very limited stock. Even if you can drive, you may, at some point, not wish to continue driving but anyway it is a nuisance having to go some distance to get to a shop or a town.
Southwold is very nice and extremely popular but it's expensive.
If it were me, I would choose the south coast. It has the most sunshine and is very clean. My personal choice would be Eastbourne. It has good amenities - shops, theatres, restaurants, a famous tennis tournament, a lovely promenade and beautiful surrounding countryside. I've found the people to be friendly and helpful too. Battle is also an attractive little town.