I think you have to have a really practical, cold-eyed look at the realities of rural living at its best, typical and worst. It's the kind of scenario where the words 'bliss' and 'heavenly' get repeated a lot, but (to me, at least) that's an idealistic view of isolated living, as is the notion that everyone leaves their doors unlocked. That really depends. A lot of my family live in rural areas, and they don't get random opportunistic theft, but they've always had targeted break-ins, both of residential properties and things like workshops, equipment sheds etc. Everything is alarmed and CCTVed. Every property has dogs. It's not Fort Knox, and it's still a beautiful, quiet area, but people take security seriously.
Being isolated is fine if nobody really registers you're there, but it's also a serious vulnerability if you come, for whatever reason, to some dodgy person's attention. Also, if there's a serious accident, you'd better hope someone is able to drive the person to hospital, as in many rural areas ambulance response times are (understandable) abysmal.
On a practical, everyday note, every member of your household will have to drive or be driven everywhere. If you've got proper lanes and there are farms around, your car will spend more time in reverse than any other gear, and your wing mirrors will always be festooned with bits of hedge.
Check the lanes around the property: I grew up in a valley village where field run-off would flood most access lanes after moderate rainfall, and then this often froze in winter, so although we weren't that far from towns, we frequently got stuck. If lanes got gritted in winter, it wasn't by the authorities: prepare to be the last priority for almost every public service.
Not many of my family's places are locatable on sat-nav, so while the thieves may find you, the Yodel driver won't.
In some rural locations you'll be able to walk out your door into beautiful countryside; in others, you'll be surrounded by in-use agricultural land and have to drive if you want to have a picturesque stroll. Also, muck-spreading really stinks, and not in a pleasantly mild barnyardy way.
Everywhere feels really dark after sunset, particularly in winter. Nice stars, but you can get tired of stumbling down potholed lanes holding a wavering torch, ducking bats. I once cycled straight into a freshly-dug trench, even with bicycle lights on.
And YY to whoever said cow coughs sound disconcertingly human! I would also add that on a dark and silent night, the sudden bleat of a sheep sounds very sinister. No: really. It's the stuff of nightmares.