I bought a 52 plate Alfa 156 2L twin spark for £560 . A small amount of rust but it all worked , 1 years MOT as well.
In answer to the OP's question.
Firstly get insurance quotes . As technically a new driver it might be the cost of the insurance is eye watering.
If you can find a policy for less than say £300 ( 3 mths ) then look for a 10 year old ish small car.
You dont state your weekly estimated milage so that makes it harder to say derv or petrol. Either way , small engined small runabout and a little odd ball . Mazda2 , Seat Ibiza or Arosa , maybe Citroen Xsara ( gopping but 306 platform )avoid Renaults as they are rubbish. Nissan Almera for example, ugly and cheap.
Try and get one with 9mths + MOT , and maybe 6mths road tax .
Its getting harder to find them due to the combination of the scappage allowance and the cost of fixing anything that requires garage time and stealershit parts.
The price of scrap metal means alot of cars are simply crushed rather than fixed at the sub £700 value. Scrap car and use funds towards another rather than cambelt + water pump plus MOT or Scrap car instead of putting in clutch and dual mass flywheel=alot of ££££.