A "plane" is a device for forming wood. "Aeroplane" or "Aircraft" should serve you better.
Best thing to do is take half a day, visit your local airfields, and look at all of the noticeboards.
And yes, it's the way ahead. Today I did 2:15 in my 1/10th of a very nice 4-seat aeroplane, this cost me £76. (Add in the £60/month I also pay in fixed costs, and I'm still winning by any standard that you care to apply). The fact that I could take it all day, with nobody worrying what I did with it so long as I didn't bend it (and if I'd wanted to take it for a week, the same would apply) and I'm winning even more.
You may however find that a lot of syndicates aren't all that keen on having hourbuilders on-board. In which case, get together with a couple of other hourbuilders and set up your own on a cheap PFA aeroplane- putting it on a convenient and cheap farmstrip. You'll still be well ahead of the game.
If you want suggestions about specific aeroplanes and airstrips, just give us all a few hints.
G