The hard drive could be on its last legs from all the swapping that must have gone on during running a game and Windows XP with 256MB.
You might consider making a PartedMagic live CD and checking out the SMART data on the drive to see if it is failing. PartedMagic also has partitioning tools that might be useful to you.
As for a distro suggestion: Puppy meets most, if not all of your requirements in post #1.
Here's a few easy-to-follow tutorials on installing Puppy. One takes you through a full install. The other tutorial is for a frugal installation.
Here's a tutorial on installing Puppy on a USB flash drive:
Introduction to Puppy Linux:
Installation on a USB Flash Disk
There's a lot of webpages about various Puppy topics. Some distros have very little info about them online.
As for your criteria:
"-easy and LIGHT installation "
"-Stability and decent speed"
check. It should run quite fast on your hardware, although I'd upgrade to 512MB RAM (or 384MB) to get the full performance with your machine.
"-the ability to run programs like Firefox, a music player that can sync to an iPod, etc."
Not sure about the ipod sync, but if the technology exists, someone has likely written a "pupplet" for it.
"-the ability to remove the Windows XP partition (I'll do that once I feel truly comfortable with the distro)"
There's a surprising amount of tools that come with the installation. I think there's partitioning tools. If not, use PartedMagic.
"-Something that can easily connect to my wireless network"
This is where Puppy absolutely excels. I've been in the passenger seat of a car driving down the street and booted Puppy as a live CD on a laptop; scanned for networks; found an open one; pulled over; established a connection; and checked my email. -all in about 12 minutes. And I don't know much at all about wireless networks. This is pointing and clicking I'm talking about, not command line expertise. But you feel like a Linux pro! Its all in the Puppy magic that the developers do behind the scenes.
"Essentially I want something good for everyday use."
I've also tried Xubuntu, and recently U-lite. If you want a Ubuntu distro, and you're thinking about Xubuntu, maybe just upgrade the RAM to 512MB and go with regular Ubuntu. Its easier to find tutorials, forums, etc. Also some people say Xubuntu isn't that much faster.
I use Ubuntu on my main daily use computer. Its a 2.8 GHz P4 with 2GB, but when I check the system monitor its usually only using around 520MB RAM and O swap. If you can upgrade your system to 768MB (256+512) you should be good to go. Puppy, Xubuntu, and many other distros do fine with less than 512MB.
I'm sure there's a distro out there that you'd be happy with. Take some of the names you see, and read their wikipedia page and check out their home page.
Also try distrowatch.com and similar sites. Although the multitude of information/distros can be overwhelming. But when you've got your operating system(s) installed, you can say you selected a distro (or two) specifically for yourself. As opposed to the MS choices: Home or Pro.