Good decision. Driving in Japan is probably not a good idea for a first time visitor there on a short visit.

That regular "rapit" train will take over 2-1/2 hours to get you from NRT to Yokosuka Station but is probably your best bet. It only runs about once or twice per hour. You could also take the more comfortable, tourist-oriented Narita Express to Tokyo Station but would then have to transfer to the JR Yokosuka Line local train in the huge, confusing Japan Station. That wouldn't really save any time - just put you in a more comfortable seat for the first half of the trip.

In your off time, plan on using local trains, subways and cabs to do your sight-seeing. Assuming you want to visit Tokyo, you will be using the Yokosuka Line to get to Tokyo and then changing to other lines. Please, please, please purchase a good guidebook for Tokyo with a printed rail and subway map. The subways and train lines will get you anywhere you want to go but are like a pile of spaghetti. Sorting out which line you need can be a challenge without some sort of map. You can also probably get one at the Tourist Information Center in the arrivals hall at NRT before arranging your train.