MvM Soldier Primary Upgrades
(Note: this post doesn't pertain to the Direct Hit or Air Strike, as they necessitate unique strategies for MvM.)
For a long time as an MvM Soldier, I focused on Reload Speed and Firing Speed Upgrades. While the DPS increase you get for your money is about the same as investing in Damage, there are a few underlying facts that should be taken into account:
1. Increasing Firing and Reload Speed also increases the rate at which you consume ammo. Unless you're using the Cow Mangler, you'll burn through ammo much faster and have to hug your team's Dispenser more often. If your team's Dispenser is gone you're in trouble, and if you're destroying a tank without the Engie's help you'll have to scrounge for ammo. Constantly running to the Dispenser is a hassle and takes you away from the fight. Though you can heal up while you do so, a bit of HP on kill and letting other classes tank damage can keep you running. The constant flow of rockets might help if you're using the Conch's HP on Hit; in that case you should use the Mangler.
2. By investing in Damage, you can take out lesser enemies in a single hit. Just two Damage upgrades can wipe out hordes of Scouts, and full damage upgrades can kill any lesser hordes aside from Soldiers and Heavies. You might fire slower, but you'll leave a helluva crater. Works well with HP on Kill; you can turn weaker hordes into walking medkits. At high damage levels, you can even ambush hordes of Uber Medics and destroy them before they can pop.
In my experience, Damage also trumps Rocket Specialist.
1. Although ignoring damage falloff is nice, by investing another 100 credits you can hit harder at any range. Use corners as cover when reloading, and give the bots any ground you can't cover; don't try to be a hero unless you're at least 80% sure it'll work. Most of the time in MvM, damage falloff isn't too bad, given the size of the maps, so getting Specialist just for this isn't worth it. Finally, consider that the Mini-Crits granted by using the Buff Banner also ignore falloff.
2. Blast Radius: The blast radius increases are rather minimal, and don't do much to increase damage. It'll help a bit against hordes but not as much as Damage would; being able to punch holes in an MvM horde is better than spreading light damage across all of them. Your teammates can help clean up any survivors. Blast radius also does very little do deter Giants; even when Giants cluster they aren't close enough to increase your damage much.
3. Stun: With damage, you can destroy them before they even become a problem. As for Giants, there are more efficient ways to slow them down: Mad Milk, Jarate, Airblast, Natasha, and Sappers. Your money is best spent elsewhere; if your team needs to buy time there are better ways to do it.
4. Rocket Speed: Again, not a very helpful mechanic. MvM is actually a great place to practice aiming rockets from afar; a bit of training on lower-level missions and you'll get the hang of it. Additionally, consider that if you invest in multiple Specialist upgrades, you'll have to constantly adjust your aim because your rockets travel faster. A bit of practice with rockets goes a long way, and makes this component of the upgrade rather unhelpful.
Let's review Rocket Specialist: Damage Falloff isn't much of an issue in MvM and can be avoided with the Buff Banner's Mini-Crits, Blast Radius contributes little damage and is useless against giants, Stun is inefficient, and Rocket Speed is unnecessary. Overall, Rocket Specialist does little to enhance performance. While you do get a small collection of otherwise forgettable bonuses for slightly less than a Damage upgrade, it's worth it to save up for something better.
I'd consider Reload Speed, Firing Speed, and Rocket Specialist to be a useful supplement to the Soldier's other Primary upgrades, but much like Burn Time for the Pyro and Charge Recharge for Demoknights, there are other upgrades that should come before it. I recommend getting at least two Damage upgrades and a backpack upgrade before considering any three of these.
