Hi.

I think you should be definately be going down the petrol route, modern diesels are not suitable for short journeys,

With regards to an automatic gearbox, you need to be a bit careful of what to buy nowadays, keep away from anything with an 'automated' manual or DSG's can be a problem, some CV auto's are very good, but most people seem to recommend the old fashioned tried and tested torque convertor box

Maybe something like a mazda 2 1,5 petrol auto (TQ box) with sat nav, but don't know if reverse camera is available,

I suppose it depends on the deals available, deposit, etc but £300 might be somewhere near the mark

Japanese or Korean and petrol powered, definitely. The Mazda 2 (or 3) woulsd be good as suggested: also I think most Hyundais and Kias have torque-converter automatics.

Recent models of the Honda Jazz have had a CVT which from all accounts is reliable.

Paying under £300 a month is of course possible in any PCP deal, but it depends on how much deposit you're able to put up. Most manufacturers' websites have a finance calculator so that you can see what deals are available on new cars: also look at the brokers such as Carfile, Carwow and Coast to Coast.