Playing a lot of Pyro, and I think I have gotten to the conclusion of this setup as not only the best for the Pyro, probably the best setup for any class over all (if that is actually possible given the variousness of the class).

Main: Degreaser. Why? Fast weapon switch, cheap airblast

Secondary: Reserve Shooter. Why? Crits on airborne targets, usefull on enemies airblasted a bit too far away or enemies jumping to avoid fire. Also, fast weapon switch, that when combined with the Degreaser you change weapons instantly - quite handy when shooting or chopping down enemies.

Melee: Axtinguisher. Why? Crits on burning players.

The Degreaser does low damage by itself, but the firedamage is not the point here. The point is to set people on fire, airblast them then to either shoot them or hit them with the axe, wich is done in less than a second. The cheap airblast on the Degreaser makes it that much better to deflect projectiles, and makes it easy to put out burning team players.

The only drawback with this setup is that you don't have any kind of long distant attack, but the Pyro is mainly a close quarters fighter anyway, so it's a cheap tradeoff in my opinion.

Playing a lot of Pyro, and I think I have gotten to the conclusion of this setup as not only the best for the Pyro, probably the best setup for any class over all (if that is actually possible given the variousness of the class).

Main: Degreaser. Why? Fast weapon switch, cheap airblast

Secondary: Reserve Shooter. Why? Crits on airborne targets, usefull on enemies airblasted a bit too far away or enemies jumping to avoid fire. Also, fast weapon switch, that when combined with the Degreaser you change weapons instantly - quite handy when shooting or chopping down enemies.

Melee: Axtinguisher. Why? Crits on burning players.

The Degreaser does low damage by itself, but the firedamage is not the point here. The point is to set people on fire, airblast them then to either shoot them or hit them with the axe, wich is done in less than a second. The cheap airblast on the Degreaser makes it that much better to deflect projectiles, and makes it easy to put out burning team players.

The only drawback with this setup is that you don't have any kind of long distant attack, but the Pyro is mainly a close quarters fighter anyway, so it's a cheap tradeoff in my opinion.

There is no " best" set up in truth. It depends on what you feel is good and your own play style. 

@The_Laughing_Man: True, but the Backburner does in my opinion not give a setup of three weapons as complete as this setup does. Flaregun? Why give away your position when you want to stay "hidden" waititng for the attack?

@HellBrendy: Why not fight off Snipers with the Flare Gun instead of getting a bullet through your mask in the split second where you think if you should ariblast and shotgun the enemy to death or burn and axe him.

There are too many situations that could be conquered by merely one setup.

I use the Detonator instead of the Reserve Shooter. I find it gives me the range the class otherwise lack. Once you learn to time the detonation blast better, snipers and scouts will rarely be a problem.

Not to mention you can set enemies afire around corners and assault them with a surprise axe rampage.

I use the detonator, because it gives you a mini rocket jump, and I've got quite experienced with jumping into places people don't expect Pyros to be and dicing them up. Also, Postal Pummeler > Axtinguisher.

Its been a while since I really played, but I remember using the Degreaser for the weapon switch and airblast, then just shooting fools with the regular shotgun. Works suprisingly well! I think I had an axtinguisher equipped, but I never melee anything ever.

The Postal Pummeler is better in every way than the Axtinguisher. FACT