score:6
First off, don't worry. Japanese train stations have extensive signposting in English and trains run like clockwork.
If it's not too late, I'd suggest changing your flights to Nagoya (Chubu/NGO) instead if at all possible. There's a direct bus from Chubu to Toyota (1:18, Β₯1750), so this would shave a good three hours off your travel time and save your/your company the bullet train fare as well (>$200).
If it is too late, I'd second the suggestion above to spend the night in Tokyo before continuing, at/near a sensible connection point like Tokyo station or Shinagawa. You can reach both on the Narita Express, and hop aboard the Shinkansen the next day.
Outside a couple of absolute peak periods like New Year and Obon (and not a concern for you in early Nov), advance bookings are not necessary for Shinkansen bullet trains. Between Tokyo and Nagoya, they run every 10 min or so and more or less always have space. More to the point, it's also expensive and difficult to book Shinkansen tickets from overseas.
Fortunately, buying tickets once in Japan is straightforward. The easiest thing is to go to the JR station in Narita Airport (English spoken) and buy a combination ticket: Narita Express to Tokyo, then Shinkansen to Nagoya. If you're staying overnight in Tokyo, ask for an unreserved ticket so you can board any train the next morning; or if you're going straight through, they can reserve a seat for you for a small surcharge.
Unless you're really pinching pennies, I'd recommend taking the fastest Nozomi express. The Puratto Kodama can only be used on the slow all-stops Kodama trains, which run only a few times per hour.
Once at Nagoya, Google Maps recommends the following approach:
And for your weekend trips, just get a personal manaca smart card, which is valid for essentially all travel in and around the Nagoya area.