Thank you, but my initial question still stands... Is Arduino a good place to start out in the realm of electronic engineering, or should I dumb it down a little first?
If you were taking Electronics Engineering in college, you wouldn't get into microprocessors until your 3rd or 4th year. But I have to agree with ChicagoDave, you should focus on what you are interested in.
The nice thing about the Arduino is that you can do quite a bit with very little understanding of electronics or microprocessors/microcontrollers.
Of course, with a microprocessor/microcontroller you also have to program, which is another field entirely. But again, programming the Arduino can be fairly simple and it can be a very-good introduction to programming. Overall, it's a LOT easier to grab an Arduino and write a blink-LED program than it is to grab some components and build a blink-LED circuit in hardware.
Im interested in starting in analog electronics... where would I go to get a solid foundation on that?
Maybe op-amps. Again in a university, you wouldn't typically study op-amps 'till you've got a year or two of basic electronics under your belt. But, you can do a lot with very simple op-amp circuits and it's OK to jump-ahead. (It would be good if you understand resistors, capacitors, and Ohms Law before you try to understand how op-amps and op-amp applications work.)
Overall, you should learn Ohm's Law and Kirchhoff's circuit laws. And, basic passive components - Resistors, Capacitors, Inductors, and how they behave in AC & DC circuits. Then, study basic semiconductors - Transistors, FETs, MOSFETs, and diodes.
For digital electronics - Basic gates (AND gates, OR, gates, etc.) and flip-flops.
If you can take more classes, that should help. You can't beat a formal class with sequence, structure, homework, feedback (quizzes & tests), plus an instructor, and fellow students to learn from. The next best way to learn is with books. The Internet is great, but it's not the best way to learn... i.e. There is enough raw information on the Internet to become a doctor but realisticlly, you have to go to medical school if you want to be a brain surgeon.