I've not used Yellow Dog, so I can't suggest a distro which would be similar to it. However, I'd personally recommend against using Fedora unless you plan to do a lot of updating - i.e., "play" with Linux. Since you'd mentioned you wanted it to be a spare PC of sorts, I'd venture you'd like something more suited to that.
Debian would be the obvious choice, in that they hardly ever use bleeding edge anything, but stick with the older, tried-and-true versions of applications, backporting patches and such as needed. Mandrake is akin to what Red Hat used to be, and is/was one of the more streamlined distros. Slackware is the "traditional" choice, if you prefer to edit configuration files yourself, rather than relying on distro-specific tools and file locations, etc. - they're likely to have a nice GUI setup nowadays, as well.
Those just a few of the more general "desktop"-type distros out there - there are a lot of others to choose from if you had something more specific in mind.
As for the networking aspect, if you're just starting out in the networking world, I highly suggest buying a set-top home router for $50-100 from Fry's Best Buy, newegg.com, etc. They allow you to share the one IP address you're usually allotted by your ISP, keep hostile systems on the 'net from connecting directly to your systems unsolicited, and usually have a built-in hub for 4-6 PCs. Linksys, D-link, and Netgear are a few decent brand-names.
As for the wireless aspect, well, books have been written about that subject. My concise advice: if you do not NEED a wireless network, don't use one.