There's no point spending much money if there's a chance you'll find cycling is not for you. Like Zoophonic I'd suggest a hybrid, but a very simple style. Go for a single chainwheel - cheap triple and doubles may give the impression of offering you more choice in gears but only add complexity and a LOT of weight. The same for gears. I'm a advocate of hub gears but they don't come in your price range, so a simple derailleur setup will do. Something simple like this Marin from Cycle Heaven in York will do the job. I'd prefer rim brakes as they're easier to adjust but getting harder to find. Nice fat (40mm) tyres for all surfaces. Only 7 gears you might say, but the range is what matters (38x34 in this case) will get you up most hills and you won't be concerned at your level by the larger gear intervals. Just get out in the fresh air, take it nice and slow and if you find yourself enjoying it you can stretch your mileage. If you're loving it after a few months you can start thinking of moving on to whatever type of bikes suits the terrain you're using most. Best of luck.
PS I'd add mudguards, but it would still be well within your budget.
Folding, Touring, Mountain, Road, City, Town, Kids and Hybrid Cycles from Cycle Heaven of York, North Yorkshire
www.cycle-heaven.co.uk