Do this shortly before you move, like a week or two. You can apply it immediately, but reapply it before you move.
Buy a really good vacuum cleaner, one with a Hepa filter or one specifically for pet hair/fur, if you don't already have one. DE (see below) is highly abrasive and the particles are very, very fine.
Buy a 10lb to 20lb sack of food grade diatomaceous earth (DE from here on) off Amazon. This one comes with an applicator. Use the applicator to apply it around all the baseboards, kitchen cabinets and drawers, dresser drawers, etc, etc, etc. Next take a dishtowel or similar cloth, lay it flat on the counter and put a handful of DE in it. Wrap it up so you have kind of a cloth bag full of DE. Now take this around to all the carpeted areas and pat the bag as you walk around. You want the DE to "poof" out into the air and form a cloud, then settle on the carpet.
You can get the DE into your electronics, but you'll want to take them apart and blow them out with compressed air after you move.
DE is not harmful to humans, you can stick a finger into it and suck the DE off the finger. It is safe for children and pets but lethal to most insects.