1. I don't think it matters for your understanding, but probably EQ is more widely applicable and useful than compression so I would go with that. It's also probably a little easier to understand.
2. That depends heavily on your setup and what you want to do. I would still say EQ is (apart from actual level setting) the most important part of mixing so not a bad place to start.
3. Practice practice practice. Groove 3 will show you the basics. Regularly compare your own sound to that of commercial cd's and try to hear why they sound different. Zoom in on the various instruments - what's going on with the guitar, with the snare drum, etc.
This is probably a never ending thing.