Learn scales first. Practice them so much. Learn the most common ones (C, F, G, etc.) first, then learn the less common ones. Once you're totally solid on all your scales, start learning chords and chord shapes. Start with normal chords, then go for 7s, major 7s, half-diminished and diminished 7s. Once you've got all that down, you can move into learning songs (melodies, bass lines, etc.) and you'll have a super solid framework for improvising, accompanying other people, or playing solo. Oh, and as far as reading sheet music goes, honestly the best way to get better is just to read a lot of music. If you know all the fundamentals intellectually, it just takes repetition to really get it ingrained. Bonus - if you read a lot of music, you'll get faster at reading music, and eventually be able to sightread most things. Disclaimer - I wish I had done this when I was learning piano, but I didn't, and I probably wouldn't have had the patience to do it. But this is (IMO) the most effective way to learn.
Sounds like the same deal as learning how to play guitar then. Thanks for the input galen and am_Unition. The thing with guitar is I haven't been the best at visualizing the key signatures and that side of it, which is a big reason why I'm taking this up. To get a better grounding on the theory and plus, who doesn't want to learn piano/keyboard/what have you. I'll be checking out that Schmitt book and look into whatever else I can find. I've got some sheet music laying around here somewhere, I'll have to dig it out.
Speaking of exercise books, check out Hanon's The Virtuoso Pianist too. As I understand it's pretty much the standard for piano exercises, and it's certainly the most useful book I ever worked out of.
I actually just found a pdf of that! After taking a quick look through it, that's something that I'm definitely going to have to work my way up to. Beyond my skill level, but it will be useful in the future.