Flamethrower
Flare gun
Fire ax
Axpyro ftw.
Actually, I usually use the axtinguisher (puff n' sting is awesome) but one night I decided to try fire ax only and have actually started to get pretty good at it. There's not much more fun than staring down a soldier across 2fort's bridge, whipping out the fire ax, jumping/riding his rockets into his face and axing him to death.
And I'm kind of surprised to hear that those who profess to be good pyros use the shotgun over the flare gun. I guess it is kind of tricky to aim. It may make you undermatched against other pyros, but they usually just flame rush you and it's not something to worry about.
You can't really scrape a lone heavy off the bridge with the shotgun, though a few flare gun shots will do it. Besides, flare gun kills are just so much fun. I suggest hitting retreating foes and sadistically thinking of the hopeless feeling they get as they burn to death. Also your team will love you if you snipe the medic.
Flamethrower because the compression blast makes you so much more versatile to the team. Saving your medic's life, saving a sentry, pushing back minefields, awesomely reflecting crit rockets into soldier's faces, and even sometimes dumb luck arrow deflect kills. Uber breaking is useful too. Still want to try rocket jumping like I saw in a video using this though =D