RE: Best Way to Store EX Cards and Other Cards of That Sort.
Applying sleeves to a card only protects it so far. After 3 layers of protection (perfect-fit sleeve -> standard sleeve -> top loader, in alternating directions), there is no real advantage to adding more. However, there are still hazards to be careful of.
Moisture can still break through just about any number of sleeves, especially in high-humidity regions, so it is generally best to keep cards in a dry place like a cellar, or a cabinet with a small passive dehumidifier in (the latter is my favorite option, because it works everywhere and isn't exorbitantly expensive). Tape can also make a reasonably good seal, but be careful not to let adhesive directly contact the card.
Temperature can also be a menace to long-term storage. High and very low temps can cause various minor effects, but the big thing to watch out for is large changes in temperature. This is usually the primary source of warping (bending), especially when transporting cards, and can be mitigated by keeping cards in a relatively well insulated, stable temperature environment. Once more, a cabinet in a heated room can do a good job at this.
The last big danger is light. Over long periods of time, exposure to sunlight can damage the ink on a card, causing it to fade and appear worn. Your best bet is to generally keep your valuable cards in a dark place, and only expose them to light when you feel like looking at them. First thought in your head should probably be "cabinet", but any place that's dark most of the time will do.
Overall, go ahead with top loaders and sleeves. You're fine with those. Be more mindful of your overall care with cards, as protection from scratches and dents is just step 1.