Hakone Pass or JR pass

I will be travelling from Tokyo to Hakone for 1 night, after which we will travel to Kyoto.
Should I activate the JR pass at Shinjuku station to Hakone then purchase Hakone free pass (3900 yen) at Odawara, or
Use Hakone free pass (5000 yen) from Shinjuku but forfeit the return leg of train back to Shinjuku as we will head to Kyoto after Hakone?

Am confused as the difference between Hakone pass with and without return Tokyo trip is only 1100 yen. But one way Shinjuku to Hakone on Shinkansen is 3400yen!

Thanks so much!

Use Hakone free pass (5000 yen) from Shinjuku but forfeit the return leg of train back to Shinjuku as we will head to Kyoto after Hakone?

No, that does not make sense. A regular one way ticket along the Odakyu Line from Shinjuku to Odawara costs only 850 yen. So, it would be cheaper to travel to Odawara by regular ticket and buy a Hakone Free Pass from there.

But one way Shinjuku to Hakone on Shinkansen is 3400yen!

There are at least four ways to go from Shinjuku to Odawara:
1) Odakyu Express: 90 minutes, 850 yen
2) Odakyu Romance Car: 70 minutes, 1720 yen
3) JR Shinjuku-Shonan Line: 90 minutes, 1450 yen
4) JR Tokaido Shinkansen via Shinagawa: 60 minutes, 3130 yen by unreserved car

Thank you so much, Uji san.

Dear Uji san
Now if we want to visit Fuji-five lakes area, which is a better itinerary, we go by Shinjuku - Fuji Lake area - Gotemba Outlet - Hakone - Kyoto, or Start off at Hakone and end up at Fuji Lake - Kyoto?

As we will not be going back to Tokyo, should we still get the Fuji Hakone pass (which has round trip) or just Hakone pass from inside Hakone area?

If we do not get the Fuji Hakone pass, how do we get around to Mt Fuji? Does the pass cover the bus to 5th Station?

Thanka so much in advance!

Now if we want to visit Fuji-five lakes area, which is a better itinerary, we go by Shinjuku - Fuji Lake area - Gotemba Outlet - Hakone - Kyoto, or Start off at Hakone

Yes, that is the best order.

As we will not be going back to Tokyo, should we still get the Fuji Hakone pass (which has round trip) or just Hakone pass from inside Hakone area?

Regular tickets in combination with a Hakone Free Pass will likely be cheaper.

If we do not get the Fuji Hakone pass, how do we get around to Mt Fuji? Does the pass cover the bus to 5th Station?

Buy regular tickets or get some local passes.

Note that even the Fuji Hakone Pass only covers the Fujikyu bus between Kawaguchiko and Gotemba and the Fujikyu train between Otsuki and Kawaguchiko. All other buses, such as retro buses, the bus the 5th Station and the buses to the west of the Fujigoko region are not covered.