I ended up choosing between Server101 (which was the one I was already looking at) and Quadra Hosting (recommended by kirby1024) as these two were the only ones that allowed multiple domains under a single account (meaning I didn't have to remember different login instructions for each domain).
In the end I went with Quadra Hosting, as they were very well priced, and their online documentation was amazing. The instruction manual for the control panel they use is available from their website, meaning that I was able to find out exactly what I could do and how to do it before I even paid a cent.
I signed up on Monday, and in the four days since, I have gotten more work done on the website than I did in the year before. So far randomevent.net (currently just a place holder and mail domain) and wowcoldblood.com (my World of Warcraft Guild site) have been transferred over, I'm currently in the process of rewriting greyblue.net (mostly a fan fiction site for a friend of mine) before I transfer it across, and I should transfer livinghistoryfestival.com (a place holder for the moment) and hitpoint.com.au (my roleplaying site, which I seem to have broken, oops) across over the weekend.
I'm currently in the process of turning greyblue.net from about 27 static pages, to 4 dynamic ones, as I am storing the stories in a MySQL database and generating the pages via php. It's proving to be a lot easier than I expected, and I'm enjoying it a lot. I hopefully should have the last page complete over the weekend, and update the DNS records to point to the new server then.
I might then start working on the "New and Improved" Hitpoint site. I have some ideas of what I would like to do with the site, and with the facilities I have at hand now, they are possible. We will see.