Scuttlebutt I hear from people who spend far too much time thinking about the intricacies of various models:
Most Hondas survive quite well over 150K miles, often with truly brutal == incompetent maintenance; many make 200K. I know of a few Acuras (Honda mfg. too) at the 300K mark. Ditto (as mentioned) Toyota Corollas generally - dunno about their expensive spreads, but ~ditto on the Maxima.
Mitsubishi - at least US versions - not quite so wonderful as has been Wade's experience with an Oz version.
BMW - I haven't enough credible info to trust; above comments are close to the impression I have. Expen$ive parts = think "boat parts".
(Disclaimer: I admit to a certain prejudice in favor of Acura, based on only a few samples of 1st-degree hearsay; lots of 2nd-degree.) Also I recently bought an 8 yo one, a 'sleeper' model (= underpriced because nobody knows about it - only ~ 30K mfg. in an unusually brief lifetime of '91-'94). You could.. get a '92 Vigor, more likely on the web - for 5K, but maybe ~135K miles = still only half-used IF not abused horribly. Stick or auto available. A clean one Is a jewel; quality throughout.
5K should get you a clean Acura Integra with ~100K mi = hardly half used-up, good brakes, handling - decent if 'sporty' ride - but 'low' = getting in & out ya gotta stoop. Consumer Reports ~ echoes the above from owner data; I believe they have never been 'bought', unlike most other sources of "unbiased" auto reliability info. Hell, for a mere 1 year guar. use - should be able to pay less than 5K for any number of OK models.
Lastly, and common to most DOHC engines nowadays: note the expen$ive Service at from 60K to 90K miles: replacing the cam/timing belt. A necessity that you or somone has done this; if it breaks, with a few exceptions == total engine disaster as pistons bend valves and maybe the rods too. [There's a link I think I could find re WHICH *few* cars are designed such that valves can't hit pistons.. even if the belt breaks] So if you aren't SURE it was done on your specimen.. well, to get close enough to tell, ya might as well replace it. Oh - usually a new water pump and various other inaccessible things are done at same job; for obv. reason. Note too: time.. is a factor; these belts ought to be renewed after 4-6 years - they are organic not steel - nuff said.
Anyway.. the cam-belt labor can set you back from $3-400 at independents to $4-900 at dealership rates. A factor in a 100K mile purchase. (push-rods? what are Those?)
For any hi-mileage auto xmission, de rigeur among the wonks is: use factory recommended auto xmission lube and Not generic. Have it flushed with a machine not just "pull plug and change". This alone can restore smooth shifting from either dirty or wrong fluids - I have some data on this last. More $$ to add to base cost.
Here's to serendipity for ya,
Ashton