Overall, I think you are in pretty good shape for making NY style pizzas. It would be nice to have a mixer with a spiral hook, but that shouldn't deter you from making pizzas with a mixer with a C-hook. My very basic KitchenAid mixer has a C-hook, and I sometimes wish it would irretrievably break down so that I could replace it with a better machine, but I have been using my mixer for over 30 years without incident.
Bread flour, such as you are likely to find in your local Safeway, is a very good choice for the NY style. I shop at a local Safeway and have been able to find the King Arthur bread flour, as well as the General Mills Better for Bread flour (which until fairly recently was also branded as Harvest King flour). Some people prefer to use a high-gluten flour for the NY style, using brands like King Arthur Sir Lancelot or All Trumps, but these flours are almost never sold at retail. You would have to order them for shipment to your home in Alaska. You are also not likely to find the Caputo 00 Pizzeria flour, or even competing brands of 00 flour, at places like Safeway. You would have to look for 00 flours at a specialty food shop, such as an Italian market. Even then, making Neapolitan style pizzas in a standard home oven is a major challenge because 00 flours in general are not well adapted to a standard home oven. You really need a very high temperature oven, such as a high-temperature wood-fired oven. My advice in this area is to master other styles of pizzas before experimenting with Neapolitan style pizzas using 00 flour in a standard home oven environment. I personally think that the NY style pizza dough is the best style to try to master. The most basic NY style dough needs only flour, water, salt and yeast and a pizza stone or tiles. You can't get more basic than that. In your case, if your budget permits, you might consider getting a Cordierite, FibraMent or comparable stone to use in lieu of tiles because of their improved oven thermodynamics.
As for trying natural starters, my advice is to master using commercial yeasts in dough formulations before migrating to natural starters. Unless you are a regular and skilled user of natural starters and preferments--like Bill/SFNM, for example--I think that you will find that starting and maintaining a natural starter takes a lot of time and effort, far more than most people are willing or able to devote to the process. I personally think that using commercial-yeast preferments, such as a poolish, is a good middle ground solution between using the straight dough process and a natural preferment. A good example is the JerryMac recipe you mentioned. Using a commercial-yeast preferment for that recipe willl save a lot of time in preparing the dough and will give you a finished product that is of high quality. Making a same-day room-temperature prefermented dough, as with JerryMac's recipe using a poolish process, will be comparable from the standpoint of crust flavor and texture to a dough that has been cold fermented in the refrigerator for several days.
If you want to avoid using a commercial-yeast preferment, you can make a straight dough using a long room-temperature fermentation (e.g., between 20-24 hours) as an alternative. However, you will need a long fermentation time to get the best results. An example of how this can be done is discussed at http://www.pizzamaking.com/forum/index.php/topic,7225.0.html
. If you want to use onlly cold fermentation, to get results reasonably comparable (but not exact) to what you will get using natural starters and commercial-yeast preferments, you would have to make a dough that can cold ferment for several days, and up to more than two weeks. I conducted several experiments along these lines, as you will see at this thread: http://www.pizzamaking.com/forum/index.php/topic,3985.0.html
Whatever dough formulation or method you use, you don't want to re-knead, re-ball or re-shape the dough when you are ready to use it. That will only mess up the gluten mesh and make the dough overly elastic and difficult to open up without tears forming. The conventional advice is to let the dough warm up for about 60-90 minutes at room temperature before shaping and stretching. If the dough is too cold, or it has endured a short fermentation time, it will be prone to elasticity and tearing. If the dough has undergone long fermentation, it may be possible to work with it without requiring as long a warm-up time.
Most of the doughs that you will see in videos, especially those made by professionals with commercial mixers, will be more robust than you will be able to make with your Artisan stand mixer. However, that doesn't mean that you can't get good results using your basic Artisan mixer. Interestingly, I have discovered that the best and most robust and beautiful looking and handling doughs I have made with my stand mixer don't necessarily produce the best crusts and pizzas. Some of the worst doughs I have made have produced some of the best crusts and pizzas. I have learned not to beat up on myself when the dough isn't perfect.