As for finding the bpm of a piece: Though there's software that claims to do this automatically, I find it the easiest to play the song in iTunes and let GB play with the metronome on until the clicks match the beat of the piece. (Although other music programs offer the possibility of "fractional" bpm like 121.75, I found that most pieces of modern music have an integer value.)
As for the audio software: The most important difference between Audacity and SoundStudio for me is that Audacity offers separate pitch and tempo shifts, i.d. you can slow down or speed up a song without affecting the pitch. Or vice versa. At least my version of SoundStudio doesn't offer this, the latest version might have it. And of course, Audacity is free while you have to pay a modest price for SoundStudio.
If you want to match the bpm of two pieces and have to do that often, you might consider one of the DJ programs that do perfectly aligned transitions automatically, even live. Do a search with "DJ" in the MacOS x section. If you only need it occasionally, doing a little bit of math and nudging the tracks until they fit might do the trick.
For soft transitions, create an overlap of the two pieces in two tracks and use the volume curves to draw "ramps" for the fading in and out.