Wheels

Full service history, size, fuel efficiency, power, condition, life span/manufacturer.

Everything else is nice to have.

Engine 

(Fred Flintstone yabba dabba doesn't look for an engine)

comfort and reliable power.  Something that isn't loud on the motorway, has enough power to over take quickly and doesn't leave you rattling after 2-3 hours on the motorway.

Oh, and heated windscreens for winter mornings.

The badge 

Whether it still has a cassette player 

got to be able to do big distances in a relaxed manner so good ride, enough power, good gearbox, good visibility

ok enough handling (the sweeter the better but I have 3 kids so there are limits)

heated seats

would love heated windscreen (darn you Ford) and heated wheel

air con

bluetoothy appy whatever all that stuff is

not too much of a bloatah

I always go for one not mentioned by an internet fantasist that works on reception for his mum. 

Service history 

Not diesel 

No cat ABCDSN whatever it is bollox

Cars are just too expensive now , even crap ones cost too much of a fortune to be messing around with that kind of risk 

Heated screens, proper spare wheel and can my dog jump into the boot.

Obviously not diesel, now because of charges, but previously because I'm not a minicab.