I live in Hants.
It's obviously exceptional because of the fact that I live here.
Ok, so far as mtb' ing goes think of it more like a big XC type environment. Ok we have lots of forests and woods and cheaky singletrack, and the Downs are on our doorstep, but.... Hilly it ain't. The Downs are lovely, no doubt about that, few bridle ways cross them (SDW excluded) so you have to join up cheaky trails to bridle ways and so on. It also gets busy in the forests, new or old "cough" and there are places I don't go because of it. QEP is a really nice place but when you've ridden it 10 times its, well, a bit meh. Then you have the parks over Chichester way and again some you can ride in some you can't.
If its riding from your doorstep you want then you can do that from any location, I do it, link 4-5hr rides off road no problem, but really it's quite flat rolling hills.
Really beautiful down here.
Don't know what you riding places are like, but think, from what you've said, it's similar, so maybe it could work for you.
Righty ho, clubs, best off joining one when you're here so Fareham Wheelers is a good place as any, Palky rides out with groups of 20odd and Tues/Thurs/Sun, great bunch, perhaps you could arrange a trip out with them to get a feel for the place. Then there's the Lordswood lot...and Muddy Moles over Chichester/Havant way..
And so on.
You don't need any bike over 120mm FS here, most ride HT's with 100mm or SS29er rigids which kinda gives you an idea of the terrain.