You don't have to spend a lot of money to get a GMRS radio. Technically, you can do it as cheaply as $25 by purchasing a BaoFeng UV-5R and calling it a day. Technically this lil' radio also covers HAM frequencies (I have my HAM technician license), but we'll be limiting ourselves to the GMRS frequencies on this trip.
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It comes with a charger. So you'll need some sort of inexpensive inverter to plug into your cigarette lighter to charge it. It wouldn't hurt to purchase a separate battery so you've always got a fully charged spare ready to go. If you can got some sort of mount for your dash so it is always in front of you and readily accessible you'll be happier. I mention the one I use by Rugged Radio later.
Even if you've got a hard-mounted GMRS radio in your vehicle, it is really nice to have a separate hand-held for when you're out of your vehicle. We spent a day trying to get through a muddy section once (with multiple vehicles quite spread out), and I was away from my Jeep a good bit, but I was still "connected" so when they needed a chainsaw or my tire inflator to reseat a bead, I heard the request.
I have an upgraded version of this UV-5R (BaoFeng BF-F8HP - $90.00) mounted on my dash using a Rugged Radio MT-5R "single side radio mount" ($17.00 on Amazon) that works well. I also have a two-way radio speaker attached to the radio (is a speaker and a mic). You can get them from Amazon starting at $15.00 (BaoFeng BF-S112); there are plenty of options for these two-say speaker/mikes. I also have the BaoFeng battery eliminator (between $9.00 and $18.00 on Amazon) so my radio is plugged into a cigarette lighter outlet all the time. I've also got an external antenna attached to the outside of the Jeep and connected to the little radio by a cable (but you could get away with the antenna that comes with the radio). So this is my version of a "hard mounted" GMRS radio. I also have a couple of the hand-held UV-5R radios for use when I'm out of the vehicle. If you are going to get a BaoFeng radio, make sure you're getting an actual "BaoFeng" product and not a knock-off.
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Midland sells a nice small/compact 15W GMRS package that includes an antenna, and I believe the power cord can plug into a cigarette lighter outlet. This is a popular GMRS radio, and perfectly suited for traveling with a group like we'll be doing:
MXT115 MicroMobile Two-Way GMRS Radio | Midland Radio (midlandusa.com)
They sell a cheaper version that's only a 5Watt radio - skip it - go for the 15Watt at least.
They also have bundles which includes the hard mounted radio and two hand-held radios with chargers. Now through 15 Jan use the code "2021" and get some off on the bundle.
ORMXT115 MicroMobile-GXT Bundle | Midland Radio (midlandusa.com)
These are just a couple of examples if you're looking for a GMRS radio. I'm just trying to present inexpensive options that'll do the job.