A forklift should be checked correctly and given a test run prior to purchasing it. This applies especially to trucks being obtained on-line. It is really important to find possible issues with trucks bought from companies on-line.
Starting the engine from cold is a great idea. Note whether there is excessive smoke and the ease with which the engine turns over. This is specifically crucial with trucks that have IC engines.
The test run should include an inspection of the truck's performance in challenging situations. A qualified driver could maneuver the truck in reverse and forward, up the ramp.
You could inspect an IC engine truck yourself. On a clear area of floor, run the truck around for several minutes while a trained operator tests the hydraulic functions. After that, examine the ground beneath for indications of fluid leakage. Even seemingly insignificant leaking can lead to serious problems which would be expensive to fix later on.
A qualified person should inspect the masts and chains. Check with and without a load that the mast works smoothly. Watch for sticking or 'binding' of the mast. A warning sign is play in the mast channels or between the mast and fork carriage. Another is creeping forward or creeping down of the mast when loaded. These could be symptoms of issues with seals, ram or valve.
The mast might have been changed at some time if the truck is not new. Make certain that the mast and any fitted attachments adhere to the rating plate on a truck. Make certain that the sideshift is not sticking when loaded.
Looking closely at the thickness of the heel for damage or wear should be included in the inspection. The manufacturer of the truck specifies minimum thickness. A loose fit could mean the carriage or hanger points are worn. Watch for cracks on the arms at heels and mountings.