I have no experience with VPNs, so appologies in advance if it's evident that I have no clue what I'm talking about.

I'm somewhat interested in the idea of creating a LAN, where every single workstation is in a different place -- in other words, a couple friends (none of which are on the physical LAN at my house) are interested in setting up a virtual LAN, for a combination of gaming and file serving. (And before anyone asks, en masse trading of MP3s is actually not the target: a couple friends and I are avid (digital) photographers, and publishing multiple directories or images to a webserver just to show them to a couple people really doesn't make sense; with a VPN-type setup, we could just save them locally and let others browse, without sharing our hard drives to the world.)

I'd guess the optimal solution would be setup a VPN here? But then, to complicate things, getting a dedicated box / colocating a server is an idea I've tossed around for a while. Which makes me wonder... would it make sense to have the VPN 'server' (if I understand correctly, VPN isn't really peer-to-peer, as there's a single VPN 'server'?) be a dedicated box, as I don't exactly have a lightning-fast connection here? Would that make sense, or is it totally weird to have people VPN'ing into a remote box?

If your connection is really that terribly slow, that's not a bad idea. You shoulud check out a program called poptop, it's pretty easy to use ...