If you sufficiently line the baskets with something like cheesecloth, the perlite shouldn't be able to get through. However it wouldn't be my first choice in a system like that either. Especially if you set it up as a flood and drain system, because perlite floats. My favorite
growing medium is "coco chips," coco fiber will fall through the slats in the baskets, but the chips are much larger particles and very few will be able to make it through. For small baskets like that 1 small brick of coco chips will be more than enough. Just 1 half cubic foot (.5 cubic feet) is almost 4 gallons worth. But you can also use
grow rocks (Hydrocorn, Lightweight Expanded Clay Aggregate). Or rockwool, however rockwool will probably water-log in a flood and drain system (suffocating roots, and causing stem rot). I haven't used it yet, but small lava rock I understand works well also (rinse it off well first). If you can find it, another one I haven't tried yet is something called "silica rock," here is a link to a post with a picture of it from a forum member that has used it;
http://www.hydroponicsonline.com/for....html#post5569