hi there,
I would do the basic checks – seatpost moves up / down ok – check for play in headset and that the gears work ok and if you can get a chain checker tool to see how worn the chain is… spin wheels and check disc rotors for any rub / check pads and tyres
Then waggle wheels to see if theres any play in bearings / any play may be the wheel or the shock bush / linkages – test for that by taking wheels out and then move the linkages etc – you will be able to feel if the pivots are tight / worn..
check the shocks work and no obvious damage or movement – inquire into service history – re forks ask when last serviced / any receipts etc – maybe budget for a service or replace the odd part… see if the shock and fork accept air ok…
do visual checks on the frame for any damage / cracks – pay attention to headtube area – see if any bad chainsuck – check dearaileur hanger and the condition of the jockey wheels = gives a good idea of wear – make sure pedals arent wrecked… go with your gut feeling re sale
cheers
paul