Decent train connection to London for friends, culture, etc would have to be high up on the list I think.
Splendid isolation sounds very appealing some days - I've always fancied a meadow of my own (with perhaps a colony of very rare beetles) - but also aware the reality could be a backwater where tractors and heroin are the main local amusements..
Set a journey time. Say, an hour. Puts you in reach of Hampshire (near London prices but great) Suffolk, a tad cheaper, Northamptonshire, cheaper still but bits are Midlands industrial (avoid the A14 corridor), Oxfordshire but prices so close to London forget it and JUST the east end of Dorset.
Depends who you are really.
New Forest is one of the 'right places to live', whereas Salisbury isn't (and mentioning crime and drugs....!). However Shaftsbury is great, Winchester ditto but pricier etc etc. If you want a small community to get welcomed into, and to live in and contribute to, then find a village. The change from London life where no-one knows who you are, and village life where everyone knows when you sneeze may or may not suit you and needs thought. Midway is the small rural town, and our best compromises were always found on the edge of a small town, where you can hide if you want or get involved if you want.
I'd have a close look at Northamptonshire. I know it well. Get North of the A14 and it's really good in bits. Look at a map and draw the triangle between Stamford, Uppingham and Oundle. Anywhere in there is lovely (with beetles), the weather is kind, all 3 of those towns pretty, old and interesting, and London is about an hour on the train. If we'd not chosen Scotland, that would have done me just fine.