I would either get a culture of fruit flies or white worms. I keep white worms myself and they're pretty easy to keep as long as your housemates (parents, roommates, spouse, etc) are ok with keeping worms in the fridge because they have to be kept cold.
Basically you can feed them anything they would eat. But you should consider whether your betta can digest the food. Crickets (I think) have more fluids than flesh under their exoskeleton. If you chop them ..... your betta would get more of the skeleton. I suggest feeding them smaller insects like fruit flies etc.
In my area people sometimes feed chopped shrimps, chicken, sausage etc. when food is scarce. What ever you feed them, consider their digestive capabilities to determine quantity and frequency of feeding.