Hello and welcome! Many of us started in tents, and moved into more comfortable accomodations! (although, I still like tents now and again!)
I don't have any specifics on your trailer model...but a good thorough inspection of everything is a good start.
One of the biggest concerns should be hunting for water damage. Inspect the roof, and all penetrating points to the unit to make sure everything is sealed. (not cracked/peeling/damaged) Roof seams, vents, plumbing stacks, anntenaes, marker lights, that sort of stuff. One tiny unchecked crack can cause more damage than you want to deal with. (mold/rot...and it can be hidden) Use all the systems to see if they work properly, and ask questions.
Also, check to see if the fridge is a Dometic. If so, check to see if it's one affected by the recall. If so, and it hasn't already been fixed...do so. (fire hazard=important!)
If it has smooth siding (fiberglass)...check for trouble. (delamination) There are some having issues with this in several makes.
If you are getting it from family, you probably know if they are keeping up with maintenance. A little preventive and annual maintenance really makes them last.
Good luck, and keep us updated.
Pete (Jolly Mon)
2014 Jayco Whitehawk 24 RBS
2004 Nissan Titan LE, 4x4