Don't take Trans-Sib-Railway ever: it's fucking boring. Russia is very good, but spending one week in a train without getting off like what many people do... doesn't make any sense. And even if you make stops for a few days in Siberian cities - well, not much to do there in winter unless to see nature or something.
Go to China without bike: you can rent it there in many cities or even buy it, if you want. China is like another planet and there are many natural wonders (mountains, caves, deserts, grasslands, whatsoever) and historical places to see: it is a huge country of civilization with 4000 years of history after all. It should be also rather cheap, if you stay there for more than two weeks because of the price of housing, food and transportation there. You can also go to Mongolia, Vietnam, Japan or even Russia's Far East from there. Guangzhou, Guilin, Kunming, Lhasa, Chengdu, Xi'an, Shanghai, Beijing - this is what you should visit and every city in this list is unique and leaves different impression. Maybe Urumqi, Hong Kong and Taiwan as well. I just don't have enough words to describe how much China is better than all the rest routes that you have on your map. It's up to you to decide though.