For what you are after, yes I'd go for Old Sarum - not particularly cheap, but not extortionate either. More to the point, it has everything you are after, including some of the best club atmosphere I've seen anywhere.
In that area, cheaper flying can be had at Thruxton, which will offer most of what you're after but is much more a school than a club. And much cheaper at Popham - which is a fantastic club, but relies upon individual (or more often group) aircraft ownership and doesn't offer ab-initio instruction.
G