New Z Owner (but with a little problem)

[ArokhX]

Salutations all. I am now the proud new owner of a 2014 370z w/ sports package! I love my new car. I love how my friends are jealous of me. I love how aggressive the car looks and powerful it sounds. I love everything about it.
But there is a problem. Three to be specific, that all can be boiled down to one particular issue. My ability (or inability more likely) to properly manipulate the clutch. This is my first ever manual transmission car. Both a good and bad situation. On one side, I believed that getting a Z in automatic would be discussing, and a disservice to the car itself. But on the flip side, I suck at it. Still, I figured that it was about time I learned how to drive manual. I just never anticipated that it would be this difficult.
Here are my three main issues:
1. Getting started from Stop to 1st – I’ve tried many a time to find that ever elusive “sweet spot” between the clutch and gas that would allow me to pull out smoothly, but to little avail (I’ve only managed it once or twice). The vast majority of the times I try to get going, I either jerk forward or stall it out completely. I’m already as tired of that burnt rubber smell as I am my push button start. It’s a cool feature sure, but when having to use it multiple times on a single trip just trying to get from A to B, it becomes a ‘button of shame’ that’s increasingly frustrating to have to push over and over again. I’ve only had ‘that one jackass’ behind me honk one time so far, but that’s more than enough for me. I so wanted to flip the bird to the impatient, inconsiderate moron behind me, but managed to restrain myself. Not sure how many more times I’ll be able to retain my composure though.
2. Shifting from 1st to 2nd – A similar problem from Stop to 1st. Just without the threat of stalling the car. Nearly every time I need to shift from 1st to 2nd, the car jerks forward and my head bobs against the seat’s head restraint. This can happen going from 2nd to 3rd as well, though not nearly as severe. Still, it’s something I wish I could avoid.
3. Reverse – Probably my toughest challenge. Especially when trying to reverse up a hill (like my driveway). Not enough gas, and the car either stalls out or starts rolling forward towards my mom’s SUV. Too much, and I come flying out the drive so fast I can barely turn enough to avoid hitting the trash can.
My mother, who is a manual transmission veteran of 40 plus years, has even said after driving the thing that the clutch on it is indeed very sensitive. She drove it in reverse out the driveway, up the hill, three point turned to come back down, then back into the driveway to park it. It still stalled on her three times during said short trip.
I love my new Z and want to get good at driving it, but this manual transmission is proving to be a big hurdle to clear. Any thoughts/advice on what I can do to better get a handle on this beast?
Thanks in advance!