I grew up in the country, but moved to the suburbs as a kid. Laws, rules, and regulations vary from area to area, so you will need to research whatever area you plan to live in. So what may be required in one place may not in another. That said, here are some things to be aware of.

If you have public roads bordering or running through your property.. you may need to maintain all bordering trees, etc... as to not risk one falling on a passing car, etc.. Some places have a crew that does it.. and they just bill the property owner. Others require you to do it. And some don't require it at all. But it is certainly something to know before buying.

If you put up NO TRESSPASSING signs on the trees that border a public road or public access way (be it a nature reserve, public park, etc), you should get no surprise visitors. But that said...

Almost everyone who lives in very rural areas owns a gun. It isn't more dangerous than living in a city.. but being so isolated and away from police, makes people tend to buy a firearm.

As for running into errant hunters or other people.. it really depends on location. But as long as you have your signs up.. it should be pretty rare.

Should be interesting to see other comments and see how it changed over the years.