On Stack Overflow: I understand that design is a different ballgame than code. However, a Q&A site geared towards helping with the tools of the trade (photoshop, illustrator) might be useful, right?
It would be, in learning tools. As a designer, it took even me a while to see the design as a separate concept from the means to invoke it—it's a very easy mistake to make, and it renders you completely blind to the slant of the particular proverbial hammer you're using. One way to get over this is to use many tools, the other, experience in many mediums; but neither can be gained without time spent. The only way to get better at design is to design, preferably in many projects, in many disciplines.
Exactly. OP, by all means learn the tools available today; you'll never be commissioned to paint a website in gouache. Just beware: it's easy to get locked in to using Illustrator and only ever coming up with things you can make in Illustrator, for example. That makes for a shitty designer.
Nothing wrong with gouache though, in fact you can learn a lot about color just messing around with some paint for a while. A lot more than you'll learn from pixels.
My advice in a nutshell: play with a lot of different mediums and look at a lot of different work if you really care about being a designer.