How about this checklist

I will take a look of this jeep this Tuesday or Wednesday. Here is a brief list I have so far

Transfer case: switch to both 4H and 4L to see if it works

Axle: Turn the front wheel to left/right most position, take a look of the axle to see if it is
in good condition

Lock: I have no idea on how to check differential lock,
can you provide a little hint?

Transmission: Engage in all gear to hear the sound

Engine: check engine oil

Suspension: Push the vehcile down on all four corners,
to see how many times of bumps it takes to recover to static status.

Rust: just look under to see if there is any rust around

You suggestion/correction is highly appreciated.