I breed crickets, mealworms and superworms plus 4 species of tropical roach and I ranch soldier fly larvae in the summer months.
Tropical roaches (recommend dubia to start or maybe discoidalis) are the easiest insect to start breeding. They don't require a lot of space and are live-bearing so there is no egg incubation to deal with. Babies can be born and raised in the same container as the adults. The two species I mentioned above cannot climb smooth plastic surfaces, so raising in a 20 gallon or larger storage container is easy.
Mealworms are the next easiest thing. My way requires a good bit of space, but results in zillions of worms. I simply move all my beetles into a new 15 qt storage container each week. Their food is the substrate (it is not true they cannot be gutloaded easily- they will happily eat anything crickets eat and were found in one lab to gutload calcium better than crickets- they are a little bit higher in fat than crickets though and have less "meat" per worm than a superworm and more exoskeleton- not a big deal but should not make up the majority of the diet) plus a bit of fresh veggies or fruit. I put a paper towel on top of the food/substrate to provide a hiding place/climbing/egg laying place. In a 15 qt container you can easily have 20,000+ mealworms. If the beetles aren't moved each week, they will eat some of the eggs and baby worms. But if you don't need a zillion like me, then it's no big deal and you can stand to loose a few to cannibalism. You could probably use a shallow substrate for your beetles and move them each week and then combine all the substrate from a single month into a single container to save space. Life cycle is 12-16 weeks, so my way requires 16 of those storage tubs, if you combine to monthly tubs you would only need 3 or 4 (just keep piling eggs or baby worms into thier siblings tubs).
Crickets are a bit more work- I collect eggs daily or adults will eat eggs. Eggs have to be incubated and kept moist. I premoisten the substrate. Vermiculite or dirt) and after collecting the eggs keep them sealed. I use food storage container (rubbermaid rectangle) 2 weeks at 84 degrees.
Crickets really require quite a bit of space IMO. Partly because it takes the babies several days to hatch and another couple weeks to all jump out of the egg containers- I'm working on that now- sanding the inside of the containers so they can climb out but not back in again. a 30 gallon clear storage tub is slippery so pinheads can't climb out and large enough for 4 egg containers, then I start another. I rough the bottom and halfway up the sides with sandpaper so the crickets can grip and climb the walls part way. Crickets live 6-8 weeks- for me a new tub every 4 days, but again, if you don't need zillions you could combine and save room. They are also very noisy- I wouldn't want them in my house.
I keep the crickets on heat tape at 85 degrees. I do the same for the mealworms, but have kept those in the past at room temp- if you only have a few lizards you don't need heat tape, they will breed fast enough for a few without it. For the crickets you will need something- heat tape or a light bulb or something. I keep the tropical roaches on a heat tape set at 95. Again- in the past I kept at lizard building temp and they would breed faster when it was warm and slower or not at all during the cool months.