I thought I'd jump in from across the dutch and add some brief comments based on the NZ Recreational GPS Society that we incorporated back in 2003, and is quite similar in philosophy to gc.com.au - except we don't have the whole alternative geocaching site thing going on. We just use yours
(I could draw an analogy to other things that Kiwi's use of Australia's but better stop here
Initially we formed a Society from completely different drivers. Some of us, as individuals, had been engaged by the Crown's primary landowner to discuss the issue of placing caches on Crown owned land. They though it was a commercial activity and that we needed to pay the Government concessions to be able to cache on Crown land. After a number of meetings I was able to get it through to them that it wasn't a commercial activity (although there were commercial opportunities around it such as gc.com). So the motivation for us was that we potentially needed to form a Society to form a legal relationship with our Department of Conservation.
Then things went quiet and we were not really sure what we were going to do for a couple of years. Over the last year, we have been getting an increasing number of requests to take geocaching to groups like Scouts, Guides and even some commercial team-building. The Society is just about to purchase some GPS units to support this and develop some promotional and educational material including a training pack. At the same time we are seeing landowners in NZ becoming interested in geocaching again, both from a positive perspective of utilising taxpayer funded facilities, but also in terms of how landowners manage geocaches. Indeed even just communicating to landowners what geocaching is and how it works is still something that we need to work on. This will probably be a guideline for local government and the like to explain everything to them. Better we do that now and help shape how local government manages geocaching, rather than have them develop a policy based on their own possibly poorly-research understanding.
From our perspective, the website is a relatively small part of what we should be doing. But during the quiet years, the membership of the Society was about keeping our websites running and building up some cash reserves for when we needed it.
For us it is much more about taking the geocaching message to the public and landowners and promoting geocaching as an activity. Naturally there is funding available for this - of course, we have to be an incorporated society to be able to apply for Govt funding. I imagine it is the same in Aussie.
Of course, it is not just geocaching for us, but also the promotion of GPS for any recreational purposes.
If you are solely wanting to fund the website, then a trust may be a suitable vehicle for investing funds, and then covering costs out of income etc. But if you want to get out in the community more, then you may have to go down the Society path. (I've been involved over the last year in the decision and helping to set up an incorporated society in Australia - unrelated domain.) If you want something democratic, then you really have to go down the Society path with elected officials and annual meetings. A bit of a pain, but it is necessary.
The first step you really need to take is to scope out exactly what you want to do. That will then guide you as to the most suitable vehicle to achieve it.