You'll have to use some sort of PC if you want to sync iTunes with your phone.
Most cases involve installing additional software on your PC that works with an app on your phone. Chances are you'll have to use a method similar to the one you use to get iTunes to work on Ubuntu to get the new software to work as well. Who knows how big of a pain that will turn out to be. Otherwise you just copy your iTunes library to your phone manually.
The next thing you can do, as charkzilla20 suggested is to change music managers. The only issue with the Google one is that you can only "pin" (download to your phone without having to stream) songs to internal storage. That means you can't use the SD card so your space is probably pretty limited. I've only searched briefly, but I can't find a really good way to sync your Android phone to Rhythmbox or Banshee. There was one thread about doing it over WiFi in Banshee but it didn't look like a very full featured sync.
No matter what you'll have to remove DRM from any songs you purchased through iTunes before April of 2009.