First, will it start.
Seriously, how well does it start. How well does it idle. Does it vibrate (that could be the prop), does it run up smoothly to full throttle, or does it hesitate along the way. At full throttle does it continue to run smoothly or does it surge or fade. Does it develop a good oil pressure. Does it sound like a thrashing machine or does it have a continuous smooth tone.
Of course, problems may not be strictly related to the engine, but a holistic test of the entire system with the engine running tells me more than reading the log books.