What are the order of kill taunts, from fastest to slowest

As nimcap answered, unusual hats are just hats with special particle effects. They have no stat benefits, only visual effects.

The only way to obtain them is to trade for them or to find one in a Mann Co Supply Crate. Crates have a low chance to contain an unusual hat.

According to data gathered by users on the forums, it seems that series 1 crates have about 2.45% chance of containing an unusual item, and series 2 crates have about a 1.5% chance. You can tell which series of crate you have by reading the tooltip.

To open the crate you need to buy a Mann Co. Supply Crate Key, which costs $2.49 in the store. If you'd rather not spend money you can trade the crate to someone. Items that come out of crates are craftable and tradeable.

You can find more details about the drop rate on the TF2 wiki page about crates. Keep in mind that this data is gathered by players and might not be totally accurate, but it's probably in the ballpark.

Ok, I did some calculations for the sniper.

First, let's consider rifles. There is always the basic version, and the fully upgraded version. We are talking about killing the tank, so upgraded means full damage, faster recharge and faster reload, as well as maximum ammo capacity. Since the damage is subject to some randomness, I averaged the lower and upper bounds each to get my values. I also assume perfect reflexes for firing as soon as the charge reaches 100%, and the auto-rezoom feature enabled.

Sniper rifle:

• Unscoped basic weapon: 33 dps (down to 24 with 15s to find new ammo)
• Scoped basic weapon: 35 dps (down to 31)
• Unscoped upgraded weapon: 107 dps (down to 85)
• Scoped upgraded weapon: 128 dps (down to 116)

Huntsman:

• Unscoped basic weapon: 26 dps (down to 16)
• Scoped basic weapon: 41 dps (down to 29)
• Unscoped upgraded weapon: 84 dps (down to 60)
• Scoped upgraded weapon: 140 dps (down to 109)

Sydney Sleeper:

• Unscoped basic weapon: 33 dps (down to 24)
• Scoped basic weapon: 40 dps (down to 34)
• Unscoped upgraded weapon: 107 dps (down to 85)
• Scoped upgraded weapon: 144 dps (down to 129)

Bazaar Bargain:

• Unscoped basic weapon: 33 dps (down to 24)
• Scoped basic weapon: 24 dps (down to 22)
• Unscoped upgraded weapon: 107 dps (down to 85)
• Scoped upgraded weapon: 90 dps (down to 84)

Machina:

• 0% charge basic weapon: 33 dps (down to 24)
• Scoped basic weapon: 40 dps (down to 35)
• 0% charge upgraded weapon: 107 dps (down to 85)
• Scoped upgraded weapon: 148 dps (down to 134)

Hitman's Heatmaker:

• Unscoped basic weapon: 27 dps (down to 19)
• Scoped basic weapon: 28 dps (down to 25)
• Unscoped upgraded weapon: 85 dps (down to 68)
• Scoped upgraded weapon: 103 dps (down to 93)

Conclusion: Whatever you do, use the Machina, it has the highest damage in all catgories. (40 is close enough to 41 - don't say anything!)

Now to consider melee weapons. I also assume the basic weapon as well as the fully upgraded weapon. Upgrades are damage +100% and hit speed +60%.

Kukri:

• Average basic: 106 dps
• Average upgraded: 296 dps

Tribalman's Shiv:

• Average basic: 53 dps
• Average upgraded: 150 dps

Bushwacka:

• Average basic: 81 dps
• Average upgraded: 228 dps

Shahanshah:

• Average basic: 80 dps
• Average upgraded: 222 dps

Now, while this far the Kukri would be best, you might notice that we forgot about one circumstance. If you are below 50% health you deal much more damage with the Shahanshah:

• Average basic: 132 dps
• Average upgraded: 369 dps

With that in mind, a stunning 369 average damage per second, while you never have to reload, makes the machina with its 148 dps look like a toy.

EDIT:

(I deleted the previous calculations concerning other classes' melee weapons, because I clearly made mistakes. I also corrected the melee calculations for the sniper, which were wrong, too. I have no idea what I did a couple days ago. I redid the melee calculations WITH critical hit chance of 15%.)