Hi and welcome to the forums,
Sounds like fun looking at the Globetrotter! The fridge might need to be "burped" [do a search for fridge and burped, might find info] especially if it has been sitting 5 years. Lots of help here if you read through the threads. There are lots of places to find parts, sometimes your local RV repair places will have what you need, other times you will need to check out the vendors here at the forum. Cheapest isn't exactly what you want, you only want to repair things once. Go for quality.
When looking at your prospective trailer be sure and check the floor. Most trailers in that vintage, after sitting out, have wood rot in the floor. Check under cabinets, etc.
Good luck! Sounds like your family is ready to travel.
Mrs. NorCal Bambi (traveling in S Tardis)