late night arrival, transportations?

Hello, i'll be arriving at the Haneda airport at 10:30pm. i was wondering what would be the best way for me to get to shinjuku station? considering how late it's going to be when i arrive

I would just take the train via Shinagawa, as explained here. If you arrive at 22:30, you are very likely to finish immigration etc. before the last train:
http://www.japan-guide.com/e/e2430.html?aFROM=2430_3011

In the unlikely case you miss the last train, there are buses until 1am.

There is an airport hotel at Haneda (Royal Park Hotel) - seems reasonably priced and I have a couple of rooms booked in April.