Hmm I would go with catching the train... the traffic can be a pain in the butt from 5pm-8pm from Narita going anywhere through and around Tokyo...
You can get your luggage couriered to your hotel/hostel, but if you are going from Narita you dont really need to worry, you will most probably get a seat on it anyway.
I've travelled into Tokyo on the train, with lots and lots of luggage, and as long as you have a seat, its not a pain. Yeah, it gets pretty cramped on the trains, but still you have a sense of your own space.
Transport and Lockers can be very very pricey, definately dont take a taxi. Also 5,000 yen is like a $50 difference.
Spending 4 days there... I dont really know where you can stay, everything is so overpriced. Internet Cafe is always good if you're on a really tight budget. hahah, dont laugh I did that for a night.