Australian passport holders currently in India travelling to Mongolia via China

We are Australian passport holders currently travelling in India. We fly to Singapore in a month to then head to Mongolia, however wanted to stop over in China if possible.

We have looked at a few options:
A) fly to Hong Kong and apply for Chinese visa there. Is there anyway to confirm cost of it when applying from there?
B) fly direct to Beijing from Singapore and apply for 72 hour transit type on arrival, however we would prefer to travel to Mongolia via train from China. Therefore does the free transit not allow for this?
C) We would prefer a tourist L, what would be the best way for us to arrange given we are currently in India?
Thanks for your help!