A quick overview of NC shows that it seems to vary County by County. And that inside incorporated City Limits is a no-no for the entire state. There are numerous references to being further than 300 feet from a habitation.
I'd love to get at least 50 acres
Eyeballing the internet, looks like farmland is running $4.1K/acre, so 50 acres is around a quarter million. Tax rate in NC looks to e 0.77%, which could be a bit of a bite come tax time. So, you might have to find a way to "work" some portion of that property so as to "earn its keep." Or get, as suggested above, various exemptions for timber, ag, natural resources, use, to control the tax burden.
That, and from personal experience, fifty acres is a lot of fence. 50 acres is a square around 1475 foot square, not quite a third of a mile. Which can seem small until you start to contemplate mowing it--even if you only mow 5 acres of it, it's a lot of mowing.
So, if the County allows (and you find the land near the right neighbors) maybe 8-10 acres suffices. Out in the ticks, there will be plenty of folk on only an acre or two who routinely just go shoot up the creek bank "out back."
There are a number of ways to get this done.