Between a 10 year old car with normal or low mileage vs 6 year old with high mileage, neither would be better than the other, it's best to go for one that is well maintained. Many parts do wear out with time rather than mileage, so it's something to take into account. Where someone who commutes a lot and does high mileage in a car, they are more likely to maintain and service it more often so it would mean that worn out parts would have been replaced...where as a 10 year old car with a low mileage owned by an OAP may have hardened bushings or seals and could have been used for very short journeys like maybe just a 5 minute journey each time to the village shop and back, hence a lot of components may not be at it's best state but it doesn't get replaced simply because the keeper is waiting on it to reach the recommended interval where it is supposed to be replaced.
As for which car to get at £1000 and diesel I'd probably go with :-
Mk1 Ford Focus, it was a good Ford, they spent a lot of money into it and they even built in Germany hoping to improve perception of the brand, it somewhat worked everywhere but in Germany. Overall a good car, at that price you're probably better off getting one with a 1.6l petrol engine. Fuel economy isn't bad, it doesn't look as dated as it's age.
Fiat Panda 1.2, probably be a bit over £1000 but you should be able to get a fairly good one. I had one before and it was a decent car, cheap parts, low fuel consumption and cute too. Only thing is I read you've got 4 kids, so it might be a problem as you won't have enough seatbelts for all of them.
The Pug 206 is fine too, I'd probably go with a fairly simple one at that price so if it does have problems it would be simple problems as well
1.4 or 1.6 HDI versions are very good engines, they are still in use today in a variety of cars, including Fords, Mazdas, Mini and PSA cars. The 1.6HDI is also used in a Mini One D, its sufficient and for the most part it does 70+ MPG on the motorway, can't complain
My guess is a 206 with the 1.4HDI should get around the same mileage and very cheap annual road tax.
Engine size, depends on the car and the driver preference