you can try this

IF({Always On/Miniseries} = "Always On" , {Total Budget (USD)}*((13-{Number (from Start Date)})/12) , {Total Budget (USD)}*{Year 1 (from Mini Series Amort) (from Start Date)})

I don't think this will work - as above I need the second part to work differently from the first, i.e. if Mini Series is selected the second line to apply.

Try this:

We can't use commas to separate functions and need to use `&`, so I replaced your comma with it; should work fine