There are many many routes, but some are cheaper than others, and most of them take a lot longer.
The fastest route isn't the one I use, but it's probably the cheapest. East Croydon to Victoria, and then the District line to Gloucester Road is faster, but a bit more expensive (actually I'm not so sure about that now, since I think I can use my Oyster PAYG card on the entire route now).
My suggestion was just what I would have done had I got that close to Wimbledon and found out the district line was out. TFL claims 16 minutes to get from Wimbledon to West Brompton on the District Line and only 25 minutes to via train to CJ and then Overground to WB.
With the district line screwed the train to CJ would have been rammed but doable, and the Overground from there to West Brompton nowhere near as busy.
Different routes from A to B will cost different amounts even with Oyster PAYG until they end the requirement to touch-out & touch-in when moving between different types of transport, as they've got no other way of working out how much money goes to each separate company (trams, SWT, London Overground, London Underground, etc). Plus there's the problem (of trams at least) of having platforms with no gates (and a system that doesn't trust people).
TFL's website says a single from East Croydon to Gloucester Road is £5.00 (peak), which I'm guessing is the obvious change at Victoria, but cheaper at £4.50 with a change at Elephant & Castle (ugh, Northern Line) or Vauxhall (not so bad Victoria Line).
Tram from East Croydon to Wimbledon is £2.70 (peak) with Oyster, from there you can go:
Gloucester Road on the tube is £2.70 peak (so that's £5.40 in total)
Earls Court is £1.30 at any time on the tube (so only £4 in total, and only half a mile extra walk past Gloucester Road).
East Croydon, Clapham Junction, West Brompton is £4 too, but leaves you an extra walk of a mile or so).
With London, it's cheaper to get the train into Zone 1 and then get the tube whilst inside Zone 1, rather than it is to get the tube from Zone 2 (or beyond) into Zone 1. Earl's Court is cheaper than Gloucester Road because it's in both Zone 1 and Zone 2, so traveling from Wimbledon you aren't paying the extra lump to enter Zone 1.