So I started learning electric guitar about 2.5 weeks ago and so far I've got down:

A C D E and G chords
Am Dm and Em chords
E5 F5 A5 B5 D5 power chords

I can also somewhat do the intros for the following songs:

Adam's Song
What's My Age Again
The Middle
Good Riddance

I figure I could keep practicing those songs, but I'd rather get more basics down first. What do you guys suggest I work on now?

At that stage I jumped into songs I liked until I got it down to learn new chords and progressions etc. I couldn't tell you if that's recommended or not.
Thanks for the advice. I think I'll start working on learning some basic scales later tonight.

Oh, I also reread my original post and realized it may sound a little arrogant, so I apologize.
Add open F chord, Scales, Barre chords. Also learning lots of songs is a good idea as you'll often come across things in songs that will push you to learn difficult chord progressions or riffs you might not otherwise have worked on.
2002 Muddy Waters Fender Telecaser (MIM) (w/ Bill Lawrence pickups & black matte pickguard)
2006 Ibanez sz520qm (w/ Grover tuners)
Epiphone DR-100

Traynor YCV50-Blue
Toneport GX / Ampltube 2
I've been doing a lot of chromatic scales to build finger strength. The stronger and more articulate your pinky and ring finger are, the easier everything else is to pick up.
pentatonic scales are probably the best thing to practice if you can play chords and songs and need to speed up and start improving
they call og or nothing at all!!
what i did when i started (and continued guitar), i used the Alfred's basic guitar method, all 6 books , some of you might not like it cause it tends to be that mary had a little lamb crap, but i didnt care, my dad's a music teacher so he told me it was the best way to learn notes, and after finishin all the books, i agree. get a method book, doesnt have to be alfreds, BUT learn stuff on the side, like ur fave songs, so that way you won't be that bored learnin that theoretical stuff when you learn stuff you like to. just my suggestion, btw scales are ftw.
definatley start with some basic scales (e.g. pentatonic) and then move on to the modes! the modes will really help you with writing your own music and learning and understanding the compositions of other artists! just keep practising!!