Yay, I'm excited you're giving Rally a try! It's lots of fun, I think you'll like it.
There are a couple of advantages to joining a training club, and I would definitely recommend taking at least one class with a club before going into competition, given that this is your first time doing any sort of dog sport.
The main benefit -- and this is something you really
need with a dog that has Issues -- is that you and your dog get used to working in an indoor venue with other working teams around. The more comfortable Gypsy feels in that environment, and the more confident you are that she'll behave appropriately (i.e., the less tension you send down the leash), the better you'll do.
A secondary benefit is that if your training club also hosts trials, you'll eventually get a home court advantage there -- your dog is super familiar with that environment and relaxed in it. This can boost your performance and scores. If you're really
good it doesn't make any difference, but, uh, most of us are not really good. Anyway I'm not.
With that said, given that you're probably just going to be learning the signs at first, and that's enough work in the beginning without adding on the distraction of managing potential reactivity, it may be best to start with the private trainer and then move into the training club's classes in January. This gives you some time to familiarize yourself with the basic exercises before you worry about the other stuff.
The only concerns I'd have with the situation you describe are: (1) make sure the signs you're learning are the ones for the venue you're eventually planning to compete in (there are four Rally venues that I know of: AKC, APDT/WCR, UKC, and C-WAGS. I think C-WAGS may just be on the East Coast, the others are nationwide, but availability of trials definitely varies by region); and
(2) try to find out how much actual trial experience your instructor has in the sport, because if you plan to compete, you eventually need/want to train with someone who is or recently has been active in that venue. Different organizations dock points for different minor details, which only matters if you care about scores, but probably at some point you're going to start caring about scores, and it's a lot easier to get something right from the beginning than go back and fix it later.
Good luck! Have fun! Rally is really about playing with your dog -- it is a very very newbie-friendly sport and (my personal insanity notwithstanding) not at all hypercompetitive. It is generally a supportive and welcoming crowd in that sport.