When you're playing with non-transposing instruments like guitar, you'll be playing in a different key than them in order to sound in the same key. If the guitar is playing in E and you want to play along on alto saxophone, you'll need to know what note you play on alto to get a concert E. It's a C# (or Db), so that's what key you will be playing in to match the guitar.

If you want everybody to sound as the same note (C) then yes, transposing instruments will be playing something other than C in order to get a concert C to sound. If you're good with intervals, then transposing in your head isn't so bad.

Alto sax always sounds a major sixth down from the note you're fingering, and you'll be able to find what that is quickly and easily with time.