From personal experience, web/print design seemed to be a lot easier than something like a logo! Logo design is by far the most difficult design niche I've encountered, simply because it's so client-specific and it packs the most design wallop for its size. They all look so simple and easy, until you try to make one from scratch yourself...
Years ago I took a bunch of introductory-level classes at Art Center College of Design, and I think their design-teaching trajectory works, because I learned a ton without feeling overwhelmed. You start just looking at shapes. One of the most interesting first-projects I did for a class was cropping out shapes out of particular fonts (we had a list we had to use, which included Clarendon, Garamond, and Helvetica). We'd choose a letter and crop it up close and see what shapes we could make. And yes, those shapes were critiqued!
Speaking of which, I probably learned the most about design just looking at typography. The more you look at different letters from different fonts, the more nuances you learn to notice - balance, curves, weight, spacing. It's easy to say "observe things" but it's different when you force yourself to actually see the disparities between two designs, especially something as subtle as typography.
Once we had done shapes, we moved on to things like posters and designing layouts for already-existing entities. That way, you already have an idea of what would look suitable. Design isn't just making something look good, you have to make it suitable for the client. In that vein, doing a personal project first will probably be easiest because you already know what would be suitable for you!