The other thing that of course helps a FRS radio a lot is height. If your son can get to the highest, clear point, it can make a huge difference in distance.
I've had to get on my roof with a GMRS (cheap hand held) radio a couple of times to make long distance coms with a friend. From my roof, with nothing in the way, we were about 8 miles apart and had a good conversation.
The used business class radios can be found for under $100.00, sometimes a lot less. Make sure you find the right model. Then you get your license, a small power supply, and antenna pole. Use LMR-400 coax for the least loss. The antenna I recommended in another post (the 14' collinear) would work great. You have to find someone to program those radios. Some sellers on e bay will program them for you before sending it to you. Just find out what frequency's and PL codes are being used by any nearby repeaters and have them program the radio for those frequency's as well as the other top GMRS frequency's. If you don't know the PL codes, 100.0 is the most common to have the channels programmed on to.
If you get one with a lot of channels, you can have different PL codes programmed and repeat the channels with different PL codes. Read the info on the site as to the rules for antennas and power output so you stay legal and do get licensed. The license will cover the whole family.
The Kenwood 840 is a good choice. Just be sure it's a UHF in the frequency range of GMRS, they come in VHF and different freq ranges also. They come in two power levels. The lower power will work great, the higher power one's usually cost more, but are within legal specs and can give more range in some cases.
Better yet, you and your son could study to get your Technician license (costs $14.00 for a lifetime each) and use 2 meters/70 meters as well as some others. Lots of repeaters with many miles of range and no requirement to learn code anymore, though it's a good thing to know. If you start your son young in Amateur radio, it can become a fantastic, life long hobby. Once you upgrade and can talk on HF, you can make contacts all over the world, it's really something.
73's John KF7VXA, WQPP214