New with high miles for me, followed closly by number of previous owners and then service history.
Me too. I'd especially avoid ultra low mileage older cars, which IMO are often very poor value for money. Cars which are not used regularly can corrode in places you don't want them to, especially inside the engine.
But the most important thing of all is condition. The current book valuing system undervalues the best cars (of which there are few), and overvalues bad ones (of which there are many).
A simple example to illustrate this - consider two three yr old cars, one completely original with 20k on the clock, the other with 35k that's just had new tyres, discs, pads, battery & exhaust. You'll likely pay a significant premium for the lower mileage car, but you'll probably have to replace all the listed parts within 18 months. The higher mileage car with everything fixed might need no more than servicing during the same period.
The cost of repairs is now sufficiently high to seriously distort the economics if you don't take proper account of what's likely to need replacing during your period of ownership. With some of the deeply discounted cheap small car deals now available on cars like the Panda & the i10, the 3yr cost of ownership may significantly favour new over used.
Older, larger cars are something of a lottery but if you can get in and out at the right time, avoiding both big workshop bills & heavy depreciation, you can travel in style for surprisingly little - but watch out for the cost of fuel.