Artale,
Welcome to the forum.
As between making a dough by hand and a bread maker, I would personally choose hand kneading. But it all depends on what kind of dough and how much of it you plan to make. Hand kneading doughs with high-gluten flour is harder to do than lower gluten flours, and especially if you plan to make a lot of dough, say, for several pizzas. Under those circumstances, either a stand mixer or food processor will do a better job.
I have experimented with making a NY style dough using a bread machine and reported on the results at Reply #51 at
http://www.pizzamaking.com/forum/index.php?topic=576.msg5486#msg5486. You might find it useful to read that posting if for no other reason than to get a feel for some of the potential problems in using a bread machine to make pizza dough (as opposed to bread dough). You might also want to take a look at the thread at
http://www.pizzamaking.com/forum/index.php/topic,937.0.html inasmuch as there was additional discussion there about using bread machines to make pizza dough.
As for flours to use to make NY style and Neapolitan style doughs, you have access to some of the better ones. The best high-gluten flour in my opinion for NY style doughs is the King Arthur Sir Lancelot flour, but you are unlikely to get it from your local sources (it may be worth inquiring however). The General Mills All Trumps flour is a good alternative for the NY style if you can't locate the KASL locally. Reportedly, Dom DeMarco of DiFaras's uses the All Trumps flour for his doughs, in combination with either the Delverde 00 flour or, if recent information is correct, the Caputo 00 pizzeria flour (the flour in the blue bag.) The Caputo and Delverde 00 flours are good flours to use for Neapolitan style pizzas because they both have relatively high protein levels. However, as between the two, the Caputo 00 flour appears to be much more popular among professionals for Neapolitan style pizzas. The Bel Aria 00 flour is also a good flour, but it is not nearly as popular as the other 00 flours among professionals, no doubt because it is relatively low in protein and gluten and doesn't tolerate long fermentation times as well. But I have had very good success with it in making pizzas where time is a factor and I don't need a long fermentation time. If you do site searches under the names of all the flours mentioned above you will find a treasure trove of information and experiences on all of the flours.
As for the starting point, you may want to think about what style of pizza most interests you and pick a good flour and a good recipe (of which there are many at this forum) and forge ahead. Good luck.
Peter
