Time to get from Narita to Shinjuku station

I am arriving into Narita at 2pm on Saturday. Will take the Narita express to Shinjuku station to catch the Romance car to Hakone-yumoto station.
If I board the Narita express by 3:30pm, what departure time should I book on the Romance car from Shinjuku to Hakone-Yumoto?
Is there enough time if the departure is at 5:40pm ?

http://www.hyperdia.com/en/
Enter 3PM for departure time. It will show 3:14 and 3:44 departures from Narita. You should be able to make the 3:14 OK.

Hi Thanks for your prompt reply. Its very helpful. However, the app's suggested route are all via shinkansen. Do you know the route via the Romance car direct from Shinjuku to Hakone-Yumoto?

There is no Shinkansen route between Shinjuku and Hakone-Yumoto. There is a Shinkansen route between Tokyo(station) and Odawara(station).

If you will ride "NEX No.32" from Narita airport(15:14), it will arrive Shinjuku at 16:39.
If you will ride "NEX No.34" from Narita airport(15:44), it will arrive Shinjuku at 17:12.
If you will ride "NEX No.36" from Narita airport(16:19), it will arrive Shinjuku at 17:44.

The connecting time between JR Shinjuku station and Odakyu Shinkuku station take about 20 mins, then you can ride on
"Hakone No.43" Romance car departs Shinjuku at 17:10, arrives Hakone-Yumoto at 18:36,
or, "Hakone No.45"(17:40 in Shinjuku), arrives Hakone-Yumoto at 19:06,
or, "Homeway No.1"(18:00 in Shinjuku) - Hakone-Yumoto(19:30).

Narita Express between Narita and Shinjuku on weekends are sometimes quite busy due to weekends schedule.

Thanks Tokyo Friend 48.

This is great help...

The NEX (Narita Express) is on the east side of Shinjuku srtation. The Odakyu railway is on the west side, but the exit is called the SOUTH exit. If you are buying only an Odakyu rail ticket you should be able to buy it at the Odakyu extrance. But if you want to buy a Hakone Free Pass I think you need to go to the Odakyu Travel office. It is also on the west side of the station but farther north.
To just buy a regular ticket should not take more than 10 minutes from the NEX to the Odakyu train.

Should I reserve or pre-book the Shinkansen ticket or just buy it on the day itself ?

Or should I buy the pass from Odakyu.jp which covers all express trains, romance car, cable car, lake boat ?

The Shinkansen and the Odakyu railway leave from different parts of Tokyo.
The Shinkansen goes only to Odawara, then you need to use the Odakyu railway to go to Hakone-Yumoto. The Shinkansen alone costs more than Y3000.
The Hakone Free Pass is good for two days.
http://www.odakyu.jp/english/deels/freepass/hakone/