I feed my roaches the veggie & fruit scraps that I used to compost: watermelon rinds, ends of lettuce, vegetable peels, etc. I used to supplement with rat block and/or cat food. They didn't eat it as well as they eat the veggies so I stopped. In the winter, I'll buy collard & turnip greens bunches and let them eat those since we don't have as much fresh fruit & veggies available.
Every summer my colony explodes and I end up giving away a lot of roaches. Their breeding slows way down in the winter which is when I feed fewer roaches anyways. I need to start swapping out the egg crates now. I do that once a year and get rid of the dirty ones.
Right now, I bet I have several thousand roaches. Yeah. Time to downsize.
Once a week, I fill up my cricket keeper with roaches to keep inside to feed my beardies (especially the babies). I like to use toilet paper rolls for them because then I can pull out the tube and shake it into the tank to get the roaches out. Very easy to do!
In my cricket keeper, I put calcium cricket water to keep them hydrated and to gut load them more.
Roaches used to creep me out. Now they don't even phase me. I'm used to them crawling on me. Roaches have a higher "meat" ratio than crickets and worms-- more protein for the price. And roaches actually smell better than crickets. Their tank smells like an earthy compost pile if it smells at all. I once had 500 crickets in a box and the smell horrified me.
When I've had a lot of baby beardies, I will buy worms to supplement their feeding so they don't wipe out the tiny roaches in my colony.
I'm not much of an expert on roaches. I'm not sure what the best ways are to start a colony, or what the optimum make to female ratio is, etc.. There are a ton of great websites out there for that. I like the fact that the roaches don't smell and don't have to be babysat all the time to grow. I ignore them and they grow. It's awesome. :)
If you have a favorite roach website, please share in the comments.