Mystery snails won't overrun tanks. They lay egg clutches above the water line, and most of the time need some help hatching. The sacs can easily be removed and thrown away.If you don't mind that your tank will get overrun with snails then mystery snails.
Nerite snail is great but they leave hard eggs on surfaces only positive thing is that they need brackish water to hatch so if you add 2 you will have only two of them
To the op: mysterys won't do much for algae anyway, they will pick at it, but it's not their main food source. Nerites will do much better for that. I agree though, try to figure out the source of your algae, such as added ferts, lots of light, etc, first. Snails won't completely solve the problem.