Four day stop in Tokyo

Hi all:
I am planning on taking a 4 day trip to Japan in May and i have done very little research on how to get around Tokyo as far as transportation. My question is, How do i conveniently get to Shinjuku from Narita airport hauling around 2 medium sized bags? Also, Should I purchase a 7-day JR Pass? Considering that i am only going to be in Japan for 4 days and i am not planning on going anywhere far from the city except maybe Yokohama. I would like to stay in Shinjuku but definitely flying in and out of Narita.

Thanks in advance for your response(s).

I am planning on taking a 4 day trip to Japan in May and i have done very little research on how to get around Tokyo as far as transportation.

There are many useful pages on japan-guide. It would be useful for you to browse this site to get a good idea and answer to all your questions.

My question is, How do i conveniently get to Shinjuku from Narita airport hauling around 2 medium sized bags?

Depends on how much "hauling" you are comfortable with. The most economical option will probably be the Suica + NEX (Narita Express) return package available for purchase at Narita.
http://www.japan-guide.com/e/e2359_002.html
You can use the Narita Express train to get you to Shinjuku Station. If your hotel is a short walk from there then that is easy, alternatively some hotels have a shuttle bus from the station to the hotel. There are also hundreds of taxis at the station, and probably only 700 yen or so to your hotel in Shinjuku from there.

Alternatively, you may prefer the bus from Narita to one of the Shinjuku Hotels, and then you can catch a taxi to your hotel if you are not staying at one of the hotels that the bus stops at.
http://www.japan-guide.com/e/e2027.html (choose to/from Shinjuku)

Also, Should I purchase a 7-day JR Pass? Considering that i am only going to be in Japan for 4 days and i am not planning on going anywhere far from the city except maybe Yokohama.

Definitely not! It would be way too expensive and massive overkill.

I would like to stay in Shinjuku but definitely flying in and out of Narita.

Shinjuku is a good area to stay and very convenient in general.

There is plenty of information on japan-guide regarding things to do in Tokyo and also Shinjuku and Yokohama of course.
http://www.japan-guide.com/e/e2164.html

Enjoy your trip!