I'm guessing your plans are all set. But as others have said, Inlaandsbanaan isn't cheap (I've taken it before. Quite interesting, you can order traditional meals and eat them when your train stops at the one house in the woods).
SJ is actually quite cheap, if you book in advance. You can get a ticket all the way to Narvik, Norway from Stockholm for under $100 US.
You might be surprised but the weather is colder than you would expect, even it being August.