If you wait until you have times for the interview, then Advances to/from Edinburgh might be the best option. Looking at the moment, these are retailing at ~£25 each way for tomorrow, ~£20 each way for next week, and ~£11 each way for a month's time. So the earlier you can book them the better, but even at just 1 day's notice that's still a good saving. An off peak day return from Edinburgh to Perth is £17.50.
Booking around a month in Advance, there are some through Advance fares right through to Perth but these are limited in availability - still it's worth checking when you get the travel times.