Hi mate, welcome to the electronics lifestyle.
As far as your questions go:
1. Electronics is a really broad topic which can range from highly technical and theoretical detailed design to fast turnaround just-make-it-work-so-i-can-move-onto-the-next-project designs. The learning approach that's best for you will depend how deep you want to get.
For me, I've found that I learn best when I'm exposed to as many new things as possible at a high level, then when I find things that interest me I can dig deeper on my own. For this, I find Chris Gammell's (and sometimes Dave's) podcast 'The Amp Hour' is great, especially the interviews.
If you're slightly more into the idea of starting with some general theory, The Art of Electronics (Horowitz & Hill) is a great, practical guide to electronics theory. There are also plenty of free options, but I'm not familiar with them.
2. First project is really important, I think. A PSU is great, but make sure you keep on top of the feature list. Make it something useful and achievable, rather than listening to far more experienced people who are telling you to add complexity you might not need. FACT: 95.7% of electronics projects are NEVER completed.
My first projects were an audio amplifier for my PC speakers (because I needed one) and an automated sprinkler controller (because I wanted one). Whatever it is you make, it won't be perfect but it'll feel great when it's done.
3. Dave's dumpster is mythical, they don't exist. But honestly, companies, schools and universities (and old engineers) accumulate crap and if you're in the right place at the right time you can snag a bargain. For the rest of us, set up search alerts on Ebay and Gumtree and wait for a deal.
James