For a £1000 you don't need to buy a banger. Its a matter of looking in the right places. Scour owner group forums. You will pick up a bargain, and pretty much guaranteed the car has been looked after.
I think there must be a tradeoff here for a £1000 car that looks the part and goes like stink. You can get a pretty decent Mondeo for less than 1k, but tax and insurance may be steep for a younger driver.
Likewise a small hatchback won't be too fast, but would be cheaper to run and insure. I'd also hazard that many used small hatchback cars would possibly be ragged silly by previous owners.
You can pick up a pretty decent Polo for less than a grand. Generally these are lower mileage, reliable and economical and looked after - lots of 'old lady owner since new' models out there.
How about this?
Volvo 740 GLE 4dr Saloon 2.3 1987
One of those colossal, built-like-a-tank volvo estates for £470!
Can't go wrong with a late 90's Polo, no crumble zones though...
A MK3 Mondeo 2000-2007 can be had for less than a grand and are solid.
Personally I would say an E39 5 Series, they are a billy bargain, build quality is amazing and cheap to insure really. These came into play in '96. I have 2 of them :)
what tax like on petrol mondeos of that era? (1.8)
Looking at the sort of things my children drive or have driven:
Lupo, Micra, Polo, Golf, Ka, Peugeot (never had any major electrics issues - mrwITch has driven Pugs for years).
Remember the insurance issue though - the most common cars have higher insurance which is why I would avoid Fiesta and Escort quite apart from any mechanical issues
Kia Swift, whilst pretty unfashionable, seems to be a pretty good car. Girlfriend picked one up for around £600 6 months ago to learn in, and it just flew through its MOT.
Not exactly speedy mind, but this might be a good thing! Tbh, at his age, I was just happy to have wheels, so a Peugeot 205 did the trick for me.