I think that your instructor is probably right, club hire systems are rarely all that amenable to more than a couple of hours use at a time. For touring, you really need to be in a group or own one outright.
There's no standard benchmark for syndicate costs, best thing is to travel around local airfields looking at noticeaboards, and take note of what's available.
I'd also suggest strongly joining the PFA. Membership will expose you to lots of other people with the same basic interest, and you'll also see lots of cheap shares or interesting aeroplanes for MUCH less money than you would inticipate (I saw a group A single seater for "£3000 or best offer") at the PFA rally. As a newbie group flying is your best starting point, but sole ownership of a permit aeroplane makes reasonable sense and there's a lot to be said for not having to deconflict availability with anybody.
G