I wish to travel to China and best budgeted way is to travel via Hong Kong. So do I need a Hong Kong transit visa for that?
Also, If I travel by train, does that require a transit visa ?
If you are an Indian passport holder, then you do not need a visa to enter Hong Kong and you are allowed to stay there for a maximum of 14 days. Please refer to the link below:
The second part of your question - I am not sure i understand it. Do you wish to travel to Hong Kong from India through train? If that is the case, I am not sure how it works. Either you pass through China or Myanmar (check visa requirements for Indians in Myanmar)
Since I do not know from which part of India you are travelling from I would recommend you take a look at this page on a travel forum for more information