I would like to write a song for a Bb clarinet. What is the easiest key for a clarinet player to play it in? Do I use the Treble clef register?
Clarinet in Bb sounds a second lower than written. Easy for the clarinet (like many non-keyboard instruments) are those having (in the instrument's key) only a small number of accidentals. When playing the clarinet, I always found the (clarinet's) keys of Eb,Bb,F,C,G,D pretty easy; this is concert key of Db,Ab,Eb,Bb,F,G. As one skill increases, more keys become easy (it's a fingering thing and to a lesser extent, just reading).
For minor keys, the equivalent relative minors are good.
Note that the clarinet has an extensive range and the the sound-quality is quite different in each range. Register breaks are usually not a problem for good (high-school band first chairs and up) players.
Yes, treble clef, transposed for a Bb instrument (i.e. for sounding C, write D).
Key isn't really an issue except for elementary players, though I wouldn't throw TOO many sharps or flats at any musician without a good reason! (And remember the clarinet will see two more sharps than the piano.)
Register is worth considering. The lowest note on clarinet is written E (sounding D) below the treble stave. The botton few notes on clarinet are a beautiful and characteristic sound, and are easy to play. It would be a pity to write a melody that had to avoid that register because it fell out of range in your chosen key. And, although clarinet CAN go pretty high, it can get a bit squeaky more than a couple of leger lines above the treble stave!