£3k really isn't much, and presumably you are not going to want to travel far to view a car at that price. So rather than come up with a list of cars which should be reliable, just go and look at cars in your area, look at their MOT histories and assuming nothing to alarming, judge on condition.
Even a car which should be reliable could be a lemon after 15 years and however many potentially neglectful owners. And for similar reasons, a car which you maybe wouldn't automatically assume to be reliable, could be a brilliant buy if it has had caring owners.
All you can do is keep it as simple as possible, n/a petrol engine, manual gearbox.
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