Today marks exactly 3 months since I got my first manual car. I had some very anxious moments, driving around the mean streets of Queens and Long Island (which are both reasonably hilly areas), but I have made major progress. I am no longer nervous about coming to a complete stop in traffic, and I take every possible opportunity to hang back and creep in 2nd or 1st instead of stopping.
Stalling is a rare occurrence, and my starts are pretty decent, about on pace with the rest of traffic. I've found that generally I rev to about 1.5K RPM to move off in traffic. I'm trying to ultimately use less RPMs, but I can't seem to move off quick enough in those cases. While my 1-2 upshift can still be felt slightly (and I'm working on improving that), it's no longer the violently shaky affair it once was. In both of these cases, I slip the clutch a little longer than when I first started driving, although it seems to be necessary for smoothness. If there's some secret to shift to 2nd gear smoothly AND quickly without slipping the clutch, please do tell

I find that my downshifts to 2nd still need improvement, although that seems to be a matter of not rev-matching perfectly. For some reason, I find that downshifts to 2nd absolutely need to be rev-matched, whereas the other gears seem to downshift quite smoothly (and no, I'm not dragging the clutch endlessly to smooth those other downshifts out).
Hill starts (which were undeniably my greatest source of anxiety) no longer terrify me and are almost second nature for me. I've had quite a few instances of uphill stop-and-go traffic, which probably helped me get better at driving uphill in small bursts. Since the drivers around don't leave any space behind me on hills, I've mostly been doing the handbrake method. When nobody's behind me, though, or the rare instance that someone acknowledged my drifting back as they approach and actually leave me a nice amount of potential roll-back space (of course, I never roll back in those instances - why would I when I have all that space?), I don't bother with the handbrake. Initially I took using the handbrake on hills as a sign of major weakness, even though I was specifically taught with that method (along with the "with your right foot on the brake, lift the clutch still it starts to shake and move your right foot to the gas" method).
I'm definitely too new to dish out amazing advice to anyone who just started (or is about to start) driving manual, but I will say that this: keep at it and don't let the frustration get to you. Also, if you are in a particularly hilly area, go out and practice some hill starts late at night or early in the morning. One one does enough hill starts, starting off on the flat will become immensely easier.
Thanks everyone on here for your support. I haven't asked many questions in awhile because I always seem to find threads where that very question has already been answered.