Welcome to the zoo, Bart. You've asked the right questions to get started on your journey. As some answers, here's my take:
1. There are no "base station" radios available for GMRS. There are 3 types of units available, Hand Held, mobile, and repeater units. Hand helds are the Walkie Talkie units which have around 5 watts of power. Mobile units can have up to 50W of output power and these are intended for vehicle installation. Repeaters are a combination of a receive and transmit unit operating o two frequencies referred to as a pair. Repeaters are available with power outputs of 10 to 50W. Units used for base stations are mobile units with an AC power supply.
2. I will assume you do have electrical power at your site, either commercial power or from a generator/solar source. You'll need this to power/charge your radios.
3. A 10W repeater such as a Retevis unit will be all you need and they are less than $400. The antenna doesn't need to be an expensive base station type. A decent mobile antenna mounted either to the roof of your camper or on a pole should be adequate. Use good coax between your repeater and antenna. The coax should be Times Microwave LMR400 or equivalent. RG-8 coax used for CB's is a definite NO-NO. You can use a pole or stand to increase your antenna height and the pole should be easy to take down and stow inside if you are worried about storm damage. Your antenna should be at least 20 feet above the ground for maximum coverage of your area. The repeater won't reach all the valleys and could be shadowed by the hill, so you'll need to test to find the dead areas.
4. Hand held units should be all you need for your area, and they don't need to be more than $35 - 40 each. You can even use less expensive units as long as they are GMRS units capable of repeater operation. All total, you are looking about $700 for the repeater, cables, antenna and pole along with the power supply. Your power supply for the repeater can be something like a https://www.amazon.com/LRS-50-12-Switching-Supply-Single-Output/dp/B019GYODX0/ref=sr_1_16?crid=3NTVXK6LBBVIR&dib=eyJ2IjoiMSJ9.upFR096NaA19tx34bdpzI_C1r7w37pkURRyOxBW8B5CNiLXEUdfa9UCqu3m5bvDCk3obEmiIizxqoOdAdyRs6dus9j4LHpl6FZUxJPZglTwN6cwZjljZyeO2n5CGP8Fp3SvEerebxcX4_idXg87gANyP0uRkV4Z4O91kPdxU2R6uDZZOsMUTKyvLhbdV3-vWjJkiof6KIRFThSvBqyWgS7peNm0noT3FweDxoxdFy9F9LhjAq9phBdLeGuiju6Guwp8YFxGsBwESG1gL6sxsca9IR38eRfggVb3YXzAco-I.r1wiDCBPB46HUAdemAyyW8lQNMNYNK3OwiTpnea6LDQ&dib_tag=se&keywords=mean+well+12+volt+power+supply&qid=1718796722&s=electronics&sprefix=mean+well12+volt+power+supply%2Celectronics%2C117&sr=1-16 should be adequate for powering the repeater.