Ya! Congratulations. I live in SF too, the hills are tricky with a stock bike. I used to have to plan my routes and strategize hitting hills at full speed.
Read up dude. There is a ton of info on this site. Jetting isn't gonna help you climb hills, unless of course your bike is capable of climbing hills and it's jetted improperly.
I've never messed with a Puch, only french bikes with glorious variators. But you should look into upgrading your clutch, a 3-shoe or something from treats. It's lighter, it'll grab at higher rpms = faster off-the-line. You could also throw a kit, which will require lots of tuning, if your new, you may want to wait till your bike is running like a top before you dive into something more complicated. Otherwise, you can port the cylinder. Also, you can change the gearing, for more low-end. This could help if you're primarily riding in the city, and you're say, only getting up to 35 or so before the next stop-light. Gearing for low end sacrifices top-end, and vise versa.
PS- you may have a rough time riding with creatures unless you kit or port your cylinder.