You have a fair point.
I'll add my 2p worth - and hopefully not confuse you more. I agree
things have changed a bit - in the old days all bikes were roadsters,
then all bikes were "racing" bikes (but not really), nowadays all bikes
are mountain bikes. A mountain bike is entry level for everyone now,
and cheapest by virtue of being common.
You've decided you want something above entry-level, and specifically
something that WORKS and is RELIABLE. I'd have said that £350 is quite
adequate, but if you go for very cheap it won't be reliable, and things
won't work without constant adjustment.
You've listed:
Mountain bikes (with and without suspension)
Road bikes
City bikes
Shoppers
Tourers
Hybrids
Comfort bikes
Well, rule out comfort bikes and shoppers, you said you like to go fast
now and again. But only now and again, so rule out road bikes. You
don't ride in town by the sound of it, so probably rule out city
bikes.
You're left with tourer, hybrid and mountain bike. You may not want a
mountain bike because there aren't any mountains. So basically you've
got the choice between drop handlebars or straight. And that depends on
how much you dislike the wind. A hybrid will be much more stable than a
tourer (until you get used to it. A tourer will be faster, is more
likely to have the gearing you're asking for, and should cope with
tracks and paths as long as you don't use very narrow tyres. Don't rule
out the mountain bike, but they very often have the low gearing you're
complaining about, and will not be as good as a hybrid on the road.