Midnight Transport-Haneda Airport to Shinjuku

Kindly please advice:

Will be touching down in Tokyo Haneda Airport at 12am.

My hotel will be near Shin O Ku Bo st. JR line (next station is Shinjuku st. )

What are the transportation will be available at this hour 12 am? Which will be the most budgeted way to reach city?

Please advice. Thanks

Shin Okubo is one stop beyond Shinjuku. Unfortunately there are not very many options if your flight touches down at 12. The last bus departures out of the airport in the direction of your hotel leave at 12:30 (shibuya) and 12:40 (shinagawa) but even those may be difficult to catch. And neither go all the way to shinjuku, so you'd have to catch a(n expensive) taxi for the last part of the journey. Which is cheaper (bus+taxi or just taxi the whole way) depends on how many people are in your party.

I'd suggest changing the hotel for the first night of your stay to somewhere closer to the airport. The Haneda Excel Tokyu for example is right in terminal 2. The room will likely be more expensive but you will probably save a lot on transportation fees.