It's really up to you what happens first. Resonance and pitch are both very important, so as long as they both get done sometimes, then the order doesn't really matter.
Anyway... I'm not actually too sure if parts of your head should be vibrating. I mean, I can definitely feel it in my jaw and chin area, but I don't remember what it was like before I had my girl voice. What I do remember is that, if done properly, the chest shouldn't vibrate much.
As for working on pitch... singing lessons and karaoke are fun, but singing well and singing poorly are no different for pitch practice. A trainer might help you reach higher pitches faster - I don't know - but, the tools are there either way. I found it was effective enough to sing along to music, trying to match the singer's pitch as best as I could.
I used this song for extra-super pitch extremity.
Her voice in that one is just... insane.
I would suggest that you practice your pitch as well as your resonance. Resonance is technique, and pitch is practice, so it's good to work on both. I would prioritize pitch if you're something of a genius, and tend to figure out vocal (or other) techniques out quickly. Resonance wouldn't be a big problem for a person like that to learn.
Another suggestion... is to do character voices. This is more of a side-thing, an optional for when you're bored. People who do them tend to have an easier time with this voice thing - I know I had a pretty easy time. I can do plenty of 'em, too, even things like Fat Albert, Watto from Star Wars, Yoda, and such. It's a blast!
