Baskets are very useful organizing tools. You can hide a lot of things in them. You can free throw doo-dads into them. You can use them as the miscellaneous files. You can even move them into another room to hide them from guests.
In the basic principles of organizing, baskets are containers. And containers are meant to be filled with things that you want to keep together because they belong together. No mish-mash. No miscellany. No maybe here now and somewhere better later.
Your baskets should be just big enough to hold the items you want to store. Any bigger and they will attract stray stuff. Any smaller and they will overflow. But what if you want to store more than one kind of thing in that basket? Compartmentalize! Divide up the basket into sections.
Add tea tins, jam jars or recyclables of any sort into the basket to divide the bigger basket into smaller groups of like items. One of my clients applied that very concept to her basket of office supplies in her craft room.
The smaller compartments within her larger basket keep her office supplies neatly grouped in small, functional sets. Her jumble of supplies is magically unjumbled.
Now, go find one of your boxes, baskets or drawers and then divide and subdivide and then divide again. It's all about creating the right-size containers for the right-size groups.