The amount of time spent in the hospital after being wounded depends on the amount of damage you take. This means that healing heavily wounded soldiers with a medkit before they leave the mission will not reduce the amount of sickleave your squaddies get -- what matters is how much they take in, not how much they leave with.
How much damage they can take in without being wounded depends entirely on what armor they're wearing. Armor provides bonus health - if they take more damage than the health bonus provided by the armor, they become wounded.
This means that adding Nano-weave Vests to your soldiers reduces the chance they need hospitalizations, even after being shot, as it gives an additional 2 hitpoints worth of "fleshwounds" they can suffer.
How much "Bonus HP" your units have is shown on the loadout screen - for example, they'll be displayed as HP 10 + 3 (combat armor + nanoweave vest).
In general, there is also an Officer Training School bonus that reduces hospital time.
That said, the simplest answer to your question? Don't get shot. The more damage you take, the longer the time off. Avoid damage as much as possible to minimize hospitalizations.
Actually those are the only two penalties to reaction shots I have encountered. At the exact second your character starts to fire, it is as if the enemy was standing there at that moment and told them to shoot and then subtract the aim penalty (-20 I think). In addition you can use this to your advantage and place a smoke where your character is dashing through. You will gain the defense boost if you are shot at while in the smoke.
Finally, I do know that there are bonuses you and enemies gain when moving or more specifically when dashing. When an enemy is dashing they are a moving target and have a higher defense and thus harder to hit. The combined reduction of accuracy from overwatch and dashing bonus from the enemy makes it very hard to hit reaction shots.
That specific perk basically removes all penalties to using overwatch on a sniper. It's pretty good when combined with squad sight.
This is all only in my experience however and I can't check what the enemy chances to hit are. I'd like to do some testing in multiplayer if possible.
Best Answer
There are not any foundry upgrades, perks, or gene mods that provide poison immunity, but you can research several armors and items that provide it
In the base game, the Titan Armor provides poison and fire immunity. In the Enemy Within expansion, The Titan Armor, Ghost Armor and Archangel Armor all provide poison, fire, and strangulation immunity.
Holding a Medkit also provides poison immunity in both the base game and the expansion. The Respirator Implant, a new item in Enemy Within, confers poison and strangulation immunity.
MEC soldiers are also immune to fire and poison, but MEC troopers are only available in the Enemy Within expansion.
So I should just outfit my whole squad with poison immunity and steamroll everyone, right?
Poison immunity is nice, however enemies will change their tactics if they are unable to poison anyone. This can make it worse for your squad than just allowing someone to get poisoned, especially if your squad is not in the late game armors with extra health. As specifically discussed on the Respirator Implant wiki page:
And since poison immunity usually comes with strangulation immunity (in Enemy Within):
So feel free to use poison immunity, just be aware of the trade-offs it provides.