Off-peak day travelcard (not valid on trains arriving at Euston or Kensington Olympia before 10.00, or valid on trains leaving Euston/Kensington Olympia between 16.45 and 18.45) is:
- £19.50 if you are willing to tie yourself to either Virgin Trains OR London Midland from Milton Keynes to Euston (or the boundary of zone 6 if you use London Midland)
- £26.00 valid on any company
An Anytime day travelcard (valid any time) is:
- £31.80 for Virgin Trains only
- £39.80 valid on any company
If you want to use the direct Southern service from Milton Keynes to East Croydon then you'll need one valid on any company, unless you are happy to buy the LM only one, which means you'll have to travel with London Midland to Harrow/Wealdstone, where you can change for Southern to East Croydon.
You can buy them online, but there is no price advantage to doing so; you are better off buying them at the station on the day as if for whatever reason you cannot travel, you won't be able to reclaim the full cost of your ticket.