You will solo 1-20 faster than you will party it, most likely. You won't be getting chain #5, but you won't be sitting on your ass waiting for a pt leader who doesn't know the first thing about blu to possibly skip over you.
Until 30, I'd go whm. The str from /war will boost your damage a bit, but your party leader will love you for healing breeze. Depending on the setup, you may not even need a whm if you go /whm as blu.
Post 30, /thf will take you the rest of the way. /nin is also useful, but all in all /thf has the leetsauce from 65+ since you get zephyr mantle.
Sorry, I know you're mainly talking about the low levels. /whm, /war, or /nin will all work. Other combos may also work if you feel like breaking out of the box.