Part exchanged my HRV (55 plate) 2 years ago, Honda have kept it and use it as a loan car, not the most economical vehicle to own mpg pathetic, road tax expensive but all offset by reliability as the only time it saw a garage was when it drove past on!
How big? For a small run-around, get a Toyota Yaris, my mum's had three and they're insanely reliable. You've get a really good one for a lot less than £10k
My wife has a 13yo Yaris, the only issue she has is the exhaust. More exhaust than normal for some reason, apart from that, service tyres etc
Any Japanese or Korean cars (bar Nissans ) are reliable to the extreme, but special prize to Suzukis. Technically they are (intentionally) behind the others as they try avoid untested new technologies until they have proven themselves. As an example, their latest cars are hybrids, but using time tested Toyota components.
No I haven't given up. I've been to look at a few cars but most of them looks like they been in a accident.