OT: new computer for eldest daughter

[SpaceBadger]

The time has come to get a new computer for my eldest daughter, and she wants a notebook PC with a wireless connection to our home LAN, so she can carry it around the house and not need a network cable connection. I haven't had any interest in wireless connections myself, so never have paid much attention to them, but I remember reading that people could get into your network remotely through the connection. How likely is this, and what can be done to guard against it? Also, what kind of range are we talking about - does someone have to be parked on the street outside your home to do this, or can they be a couple miles away? (We live out on a country road and random passerby looking for open wireless connections seem unlikely.)

Then once I get this worked out, I still need to figure out how to arrange her net access so that she can trade emails with friends and do research on the web, without opening her up to the vast cesspool of unrestricted internet.

Losing sleep over this. Any help/suggestions appreciated.

SpaceBadger