The insect you saw could be a small grasshopper or it could be a katydid. Both of them feed on plants and both start out as very small individuals.

I've had good results using neem oil on my plants. It acts as an antifeedant for those pesky plant pests. It might not kill them outright, but does keep them from chowing down. Very little collateral damage to beneficial critters.

Get a 2 liter cola bottle, fill it with hot water, drop in 4 cloves of smashed garlic, put it in the hot summer sun and let it sit a week. Strain out the garlic but keep the water. Use a cup of garlic water and 3 cups water in your bug sprayer and spray the plants. That will get rid of the critters.

I had the same problem with my basil plants. I tried several methods involving insecticidal soap and even chili powder that did not help. One day I went out of town and put a bunch of potted plants around my basil (above soil) to make it easier for my neighbor to water my plants, solved the problem completely. I happened to have several papaya plants growing in milk jugs. I was out of town for a month, when I came back the basil was perfect.

If you choose neem oil it's best to keep your plants out of the sun for a while. So spraying around sunset is best.