If you're going for absolute privacy and peace I'd get 100 minimum, 200 if you can. And I'd make sure there's no easements for people to drive though (like to reach another property on the other side).
I got 40 thinking it was a lot, well I ended up buying the adjacent lot to keep it from being subdivided and possibly turning into a trailer park. It's really not far away at all. And now the neighbor is selling the lot on the other side but wants $2000 an acre. If he comes down I may buy it but it would have to come down in price a lot. That would put me right around 100 acres.
And here i was thinking 100 was plenty.
:-)
Well it was just my experience, it could depend on the landscape and other factors. But where am I had to spend more $$$ to keep from having a close neighbor or 5. And I was lucky to get it before anyone else could.
In case you're looking for more land:
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