The #1 best way to store the pictures is to scan the slides as soon as possible and save multiple copies of the digital files in multiple places. Slides will degrade. The only question is how fast.
There are various degradation mechanisms of slides.
One is that the dyes simply fade. As with most chemical processes, lower temperature slows this down. The film type makes a difference here. Kodachrome, for example, fades much slower than others.
Another degradation mechanism is mold. Here the main drivers are heat and humidity. You also want to keep mold from spreading when the inevitable single mold spores grow and eventually make more mold spores. So here the defenses are cool, dry, and physical separation or barrier.
Note that cool is good for both, so that's a no-brainer. However, humidity is also very important. A damp basement, even if relatively cool, is a really bad place for slides. Really really dry air can have negative effects on the dyes and the gelatin, so somewhere in the 30-50% humidity range is usually reasonable.
Anecdote
My mother stored many slides in her basement. These ranged from the 1940s to the late 1970s. While that was the overall coolest part of the house, it was also the most moist. She didn't have a dehumidifier down there, so in the summer the humidity was probably close to 100% for months. Many of the slides were in bad shape when I inherited them in 2013.
The oldest slides had faded. However, with a modern scanner, it is remarkable what you can recover from faded pictures. You start by making the darkest part of the scan black and the lightest white. That by itself goes a long way to adjusting for the fading. You usually have to do a custom non-linear curve per slide, and fiddle with the color balance of the mid-tones. In the end, there is still some loss, but with a little care, you can make digital versions that look much better than the original faded slides.
The real problem is the mold. No, wrapping everything in plastic doesn't prevent moisture from getting in. Water will diffuse thru just about anything given enough time. What a "impermeable" layer does is slow down the exchange of water with the ambient air, resulting in roughly average humidity inside. This can be really bad for slides, paper, and many other things in a non-dehumidified basement in a temperate climate.
One thing I noticed is that the slides stored in slide trays had significantly less mold on them than the ones stored in boxes right up against each other. This seems to be the main driver for the extent of the mold damage, not the age of the slide. My guess is that the larger physical separation distance made the difference. Mold spores from one slide simply had a harder time getting to the next slide.
Again, though, slides will degrade over time, no matter what you do. Scan them now.
