Well I've had my Fender Squire for a little over a month now, and I've been playing it almost every day for at least an hour. I've gone through the beginner's DVD and learned about power chords, major/minor/dominant chords, and moveable chords, I've practiced moving between all of them (not so much dominant chords though), and my movement is becoming noticably better.

So I'm really just wondering what I should focus on next, I've already learned a few Avril Lavigne and Blink songs, along with a little Weezer, but I feel like I should try and perfect my technique first before trying to learn a lot of songs- that way it'll be easier for me to go about learning the song. I've also been playing the Tuba for 6 years, so I know a lot of music theory already (intervals, key sigs, chord structures, etc.). I was wondering if I should start learning some scales? Also, is there anything I can play to help practice my palm muting?

For your palm muting, you can check out some Metallica. An easy-tempoed song for palm-muting would be Seek and Destroy.
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scales would be an excellent idea

I agree with this guy, learning the where to play the scales on the guitar, would be a good idea. As for your technique, it al depends on what technique your going for. If your working on bends and pull offs, it might be best to learn a song that consist of those. Start practicing slow, and build your speed up. Now if referring to different type of picking, then I'd advise you start practicing some exercises.

Either way, good luck.
definitely scales. and you should learn a few beatles songs. they have fun and somtimes challenging chord transitions. thats what i started playing at least