Backpacking South India for 4-6 weeks - tips?

I'd heartily recommend booking your train ticket from Mumbai southwards ASAP - like before you get to India.
Otherwise you may well find yourself waiting for a space on a train for a few days watching all your holiday cash disappear in costly Mumbai.
Dr.Dandapani in Wembley (listed here http://www.indianrail.gov.in/international_Tourist.html) is where I booked mine, although you may be able to do it online now for all I know.
Once you're elsewhere in India though it's a piece of piss to get tickets.

http://www.cleartrip.com is excellent for booking indian railways tickets.
+1 for booking trains to Goa well in advance - otherwise you may end up on the overnight bus which is an experience I wouldn't wish on anyone.