Hi,
An issue you have is that you want to mix road and off-road. Mountain bikes - though popular on the road - are are waste on tarmac. They'll be slow, heavy etc. When you say, wooded areas, do you mean jumping rocks and logs, or just pootling on packed earth? If it's the latter, a hybrid may be better.
The term hybrid covers a lot of bikes, but in this case I mean a mountain bike style frame with larger road-type wheels (700c size rather than mountain bike 26inch) and thinner tyres. This will be fine through the woods and much much faster and easier on road.
The other issue is suspension. You do NOT want full suspension bikes. Full sussers are for cycling up and falling off of mountains. Like me, you live in Norfolk.....! Also, a decent full susser starts at about £1000 so any cheaper than that are toy bikes from catalogue shops
Now, some folks will get front suspension, but again, it can be OTT as it will waste effort going along normal roads. But then again, if you're not planning on haring along and if you're going through the woods a fair bit, it might smooth the ride out. Most folks say front suspension makes going up hill a lot harder (as your effort goes into 'bouncing' rather than progressing) but not many hills around here.... Note though, if the bike has front suspension, then the components will be of a lower quality compared to a similarly priced bike without front suspension.
Now makes, at this sort of price, all the bikes are effectively made in the same Asian factories with similar components - so it's more a matter of trying a few out from the more respected makes.
So try out 700c wheel hybrids (with or without front suspension) from companies like Trek, Specialized, Giant, Scott, Kona, Cube, Claud Butler.
For those sorts of bikes, the shops in Norwich I would recommend are Pedal Revolution, Cycles UK (Jarrolds), Streetwise (Nelson Street), John Borwell (Spencer Street).
I would normally say steer clear of
Halfords, but the Halfords Metro (Castle Street) in the city centre are quite good and they did have some ridiculously discounted 2009 Kona Dew hybrid bikes a month ago - so that would be worth a look.