I own three domains. This one and two other undeveloped ones. I didn't expect to start development on those websites when I bought them, though. I bought them to prevent someone else from buying them later on down the road and so that if I ever do decide to pursue the ideas I have for them, I'll be able to do so, unencumbered.
As for the money involved... well, you wouldn't, in theory, even necessarily need to pay for it. If you wanted to have a free domain name (eg. roadkill.noip.org, or something), you could. You could also host it on your own computer. Wouldn't get spectacular speeds, mind you, but that may not be a problem for you (or maybe it is a problem... who knows).
But if you wanted to get a "real" domain name and have a more reliable host, you'd need to pay. The cheapest hosting option would be shared hosting. The cheapest option frostjedi.com's host offers is $60.00 / yr:http://www.surpasshosting.com/hostingplans.php
As for whether or not $60.00 / yr would be a huge waste of money... well, around here, internet costs $50.00 / month, or $600.00 / year. It's cheaper then that by leaps and bounds.
As for what to do with it... a blog or a "stupid webpage" would work. You could, if nothing else, use it as a testing ground for stuff. You could mess around with creating your own PHP scripts, or modifying WordPress, phpBB, MediaWiki, or whatever else. You could use it to share files with friends / family members - files that might be too large for email, as well.
And yeah... starting a forum is going to be tough. Not because the software is tough to install, mind you, but because it's going to be tough to keep it alive. CR has spawned a ton of message boards, FJ included, and of those, afaik, only FJ is still around. And most of those others never got above 2,000 posts.
Might be worthwhile as an experiment, though. And who knows - maybe it would be successful.