I don't know what you mean by limited but I did have a dedicated server with 2003 Web edition and I could use it just fine.
I had Filezilla ftp server installed, apache, php, mysql, some newsgroup software, even used it to seed some legal content on a torrent tracker.
If I remember correctly, Windows 2003 Web edition is limited to 2 GB of memory and one processor. In addition, you can't install Microsoft SQL server but I didn't care anyway.
For your needs, 2008 is not needed, i mean it wouldn't make any difference however, some companies only offer 2008 Web nowadays.
cwebcweb, I'd suggest trying out one of Leaseweb's ultra green servers - the servers in this series come with Windows free (well, the Web edition):
Just wait a day or so and check once in a while to see what other dedicated serves pop up there, right now there's only two, relatively weak performance-wise.
This way you won't feel sorry about spending money on Windows, as it would be free anyway.