I must say I'm not terribly keen on this new series of Doctor Who, the last episode wasn't bad but I think it's lost the ability to tell a good story inside of 45 minutes, possibly too much emphasis on trying to tell an arc story over 13 episodes.
Fortunately BBC4 Xtra is broadcasting some of the Big Finish Doctor Who adventures late at night and then making them available for streaming on iPlayer later. The episodes don't hang about forever but there seem to be a few Silvester McCoy ones about at the moment:
A Thousand Tiny Wings has episodes 2 and 3 of 3 available
and
Survival of the Fittest Which is not the ones with leopard people and Ace but is an original drama and still mid-broadcast (Episode 1 actually explains the doctor's new companion, which might help you as a primer with A Thousand Tiny Wings)