What are the unbox rates for the new Weapon Cases

Note: I don't play Heavy a lot, so this is mainly observation from watching others play Heavy.

Heavy builds tend to vary depending on the types of enemies you're facing.

The standard "medic buddy" offensive build is this:

• Minigun (or Iron Curtain, which is a reskin of it)
• Shotgun or Sandvich
• Fists

The standard "medic buddy" defensive build is this:

• Minigun
• Shotgun or Sandvich
• Fists or Fists of Steel

Note: If you're having problems with lots of Scouts, swap the Minigun out for the Natascha.

Note 2: The new weapons aren't listed here simply because they're new and some people are still getting them... and thus they haven't been tested that much.

A new Offensive build may be:

• Tomislav
• Sandvich
• Fists or Gloves of Running Urgently

or

• Minigun
• The Family Business
• Fists or Gloves of Running Urgently

Defensive build is likely better unchanged from standard.

Now, as for the items above:

Primary Weapon

The standard Minigun is - in most cases - the optimum choice, offering good spin-up, range and damage.

In general, the Brass Beast makes you move too slowly when shooting it and the spin-up time is too long. Its drawbacks are too great and a Heavy vs Heavy battle will likely go to the other Heavy if they manage to surprise you. Also, the weaker classes already die quickly enough to the standard Minigun.

The Tomislav is a minigun with no spinning sound (although it does make a noise when you raise or lower it) and it spins up faster. This can replace the need for the Shotgun in your build, as your spinup time is decreased by 40%.

Secondary Weapon

The Sandvich is a controversial choice. Generally, you have it so you can throw it to your Medic if his Health is low. However, you lose your Shotgun, and the Shotgun is both a good backup weapon, and a good weapon to have equipped in case someone surprises you on the way to the battle front.

The Second Banana (from the Jungle Inferno update) is used to similar effect. The heals it provides are less than the Sandvich, but in the time a player consumes and recharges their first Sandvich, you will have a third banana on cool down, giving you larger heal per second than Sandvich, but lower "burst heal".

I've seen at least one person who mains Heavy switch out his Shotgun for the The Family Business. It does slightly lower damage, but you have 8 shots before reloading rather than 6 with the regular Shotgun.

Melee Weapon

Largely, the melee weapon isn't used that often by the Heavy. Therefore, choose it based on its effects.

The Gloves of Running Urgently is a good choice for offensive if the team has no teleporters, because you can get to the front lines faster with it. However, its immediate 20HP drop when equipped and then further -10 health per second drain leaves makes you much easier to kill if ambushed on your way there. (Note that your health will not decay below 100)

The Fists of Steel is useful if your Medic has died and you need to escape due to the reduced damage taken from ranged weapons.

According to an interesting forum post describing the advantage of the degreaser, the default switch time is 0.67 seconds.

As far as I know only the Degreaser (65% faster, 0.67(1-0.65) = 0.2345 seconds) and Reserve Shooter (15% faster, 0.67(1-0.15) = 0.5695 seconds) can affect this, besides the weapon-specific limitations as mentioned in Toomai's answer. Also of course the Half-Zatoichi is 'honorbound' and has a switch time as long as it takes you to get a kill!