I did my first logged flight out of Blackbushe a decade ago now. It's a perfectly good little airfield for learning. A little busy at the weekends and you'll get to mix with a fair bit of small bizjets, King Airs and helis.
A close school is handy for flying in so far as you have lower petrol costs and you can see the weather.
A further school may save you ££s per hour (important later on in the course when you may be doing 2-3 hours a day) but you have driving time and wasted journeys to the airfield on "marginal" weather days. (Or you stay at home on a day that turns out to be nice).
Good luck