Even before I bought my first DSLR, I'd read up about the "exposure triangle" so I understood the concepts and how changing each of the three setting would affect the photo. This meant when I got the camera I felt confident enough to go straight into the semi-auto modes (aperture priority and shutter priority).
Don't worry about learning advanced techniques to start with - just understand the basics of aperture, shutter speed and ISO. Once you're got those, other things you read will make more sense, and you'll also have more of an idea how to get the shot you "see" in your head. Also, don't feel you need to use manual to be a "real" photographer. I only use manual for <0.5% of my photos (not that I'm any good...).
The important thing to remember is that it's the settings that matter, NOT WHICH MODE YOU USE TO GET THERE! ISO 200, f/2.8 and 1/60s takes the same photo regardless of whether you set it all manually, use A or S, or even the camera picked it all for you.
That said, I have a basic rule of thumb for picking the mode to use. I think about what is the most important effect I'm going for;
1. Want to control depth of field accurately? (especially if you want shallow DOF for eg a portrait). Use aperture priority, set the aperture for the DOF you want, let camera handle the shutter speed. Up to you if you want to manually set the ISO or use auto-ISO (depends on how your camera behaves compared to what you want it to do - some try to keep ISO down and increase shutter speed, some are more trigger-happy with the ISO). Exposure a bit off? Use exposure compensation and take again.
2. Want to control/eliminate motion-blur? Go for shutter priority. Set the shutter speed to get the right amount of "freezing the action" as you want, let the camera handle the rest. Exposure a bit off? Use exposure compensation and take again.
3. Camera making a pig's ear of it? E.g. you want to control two inputs and camera isn't reading your mind? Time to go for Program mode or manual.
4. Everything else - up to you. Full Auto isn't to be sniffed at (cameras are surprisingly clever), but most of the time I just set it to aperture priority and a middle-of-the-road aperture to grab a spur-of-the-moment shot. That's because I use A-priority for maybe >90% of my shots so it's just easier to be in that mode as a starting point.
Final point in a rambling post - digital photography has cheap running costs once you've got over the initial outlay on kit. Don't be afraid of taking the same photo with various different settings and seeing what works for you. Take your time, and expect to take many, many duff shots. Hit delete, tweak your settings and try again.
