Any car you buy for less than 5k wll have to be treated as a banger and at that level of daily mileage you’ll probably have it fail at least once a year with something.
I killed a Rover (not that difficult really) twice in two years on an Ipswich to Cambridge daily commute (150 miles round trip daily give or take) and it was costing me enough that I ended up moving nearer to work.
Of the two options above though, I’d go for diesel for simplicity, but I think that LPG may end up being the slightly cheaper option. Unless it breaks, in which case it might be more expensive.
Alternatively, buy two or three very cheap cars and rotate them during the week. Then if one dies, simply switch to another car.