But wouldn't both go off in opposite directions? Obviously, the person shooting won't go as fast due to much greater mass, but there would still be motion.

m1 * v1 = m2 * v2

The mass (m1) of the bullet is a fraction of a percent of the mass (m2) of the astronaut. So let's say (generously) that a 9mm slug weighs about 10 grams. A 200 pound astronaut is equivalent to about 90,000 grams. That means that the resulting velocity (v2) of the astronaut would be 1/9000th of the velocity of the slug, or in other words, if that 9mm bullet travels about 1500 ft/s, the astronaut would be knocked back at about 1500/9000 = 0.16666667 ft/s. It would take 12 seconds for the recoil to move the astronaut one foot. Hardly something that would create great difficulty for the shooter. Besides all of that, the station is pretty close quarters, it would be easy for the shooter to brace himself against a solid surface to prevent any kind of recoil effects.

Incidentally, that would be the same reaction as on Earth. Being in zero-G has nothing to do with the simple physics of the situation.

Since it's the propellant that causes the bullet to be propelled, it's similarly responsible for the reaction of the astronaut. The propellant pushes both the bullet and the astronaut with equal force. Force equals mass times velocity, so the equation still reduces to the simple conservation of momentum equation I showed above.

I realized a slight error in what I said above, but I don't think it has a significant effect on the outcome... Force = mass * acceleration, not Force = mass * velocity. Basically, if you expand the expressions and consider the reactions to be happening over the same period of time "t" (which would, for all practical purposes be the time from the ignition of the powder until the slug exits the barrel of the gun... a fairly short time), you get:

F1 = F2 (from Newton's Third Law - every action has an equal and opposite reaction)
F1 = m1 * a1 = m1 * v1/t (Newton's Second Law - F=m*a)
F2 = m2 * a2 = m2 * v2/t (Newton's Second Law - F=m*a)
m1 * v1/t = m2 * v2/t

Multiply both sides by t, and you get m1 * v1 = m2 * v2. This is actually the Aristotelian model, which is a subset or gross simplification of Newtonian physics that works, but only because it discounts many other forces like friction.

Propellant expends most of its energy accelerating the mass of the bullet.

To be fair, the propellant expanding is also accelerating the mass of the astronaut... it's part of the conservation of energy. However, as I said, the disparity between the masses of the bullet and the astronaut tends to mean that the bullet will be accelerated to pretty much the same speed as it would have in Earth's gravity - the reaction seen as recoil would not be dramatic. Certainly the astronaut wouldn't go hurtling backwards or anything.

To quibble on the subject of the mass of the gas (just for the sake of discussion, I'm not trying to beat a dead horse), let's say it's factored into the weight of the bullet (a typical 9mm slug itself weighs a bit less than 10g, more like 7-8g, and I rounded it up to 10 to make the numbers easy for purposes of illustration). The mass of gas used to expel the slug is not really significant (just the tiny amount sealed inside the bullet casing, which wouldn't be measured in grams)... I think what you're confusing in there is the energy being added by the chemical reaction. That reaction (ignition of the powder) takes a still relatively small amount of gas and gives it quite a bit of energy... but it's still a very, very small contribution to the impulse acting on the astronaut, even if you consider the gas to be moving faster than the slug, or were looking at just the gas ejected from the barrel without a slug... the much smaller mass of gases, even moving at much higher speeds than 1500fps, imparts less force by itself than the force imparted by the bullet speeding down the barrel, pushing back on the expanding gas, which then pushes back against the chamber of the gun and so transfers the energy to the astronaut.

If that were the case, then wouldn't a tranquilizer gun or just a tazer be more sensible? Higher chance of subduing the apeshit astronaut without killing him (and then he can be restrained) or without risk of putting holes in the station itself. To quote a fictional Russian submarine captain.... "things in here don't react well to bullets."