When feeeding our insects (crickets/roaches/superworms) our dry diet, we go with the following veggies: squash (yellow, winter varieties); carrots; pumpkin; sweet potatoes. Avoid spinach & cabbages.
We also use fruits such as pears, apples and melons. You want firm-flesh fruits - not something that could turn mushy in 24-48 hours (like peaches; plums and similar fruits). We occasionally give oranges or tangelos.
For us, the rule of thumb is neatness because we have so many to feed. Another thing we discovered: no matter if you do give carrots or some other veggie/fruit for moisture - they still want a water source. We use water gel exclusively. It's cheap and easy. You can even rinse it off if it gets a bit soiled by crickets - but we found that the secret is using smaller dishes.
Early on, when were only feeding a couple thousand crickets, we gave them all the kitchen scraps - breads; veggies; fruits; meats (crickets are carnivorous whereas the roach isn't). Once we developed our insect diet, there wasn't much need for too many extras.
When gutloading crickets or roaches I use collard greens, turnip greens, mustard greens and dandelion greens. I use acorn, yellow and green squash. I use zucchini, escarole, endive, sweet potato, carrots and the occasional banana. I don't use a lot of fruit as it has a lot of sugar.
This site has a great list of nutritional facts of common reptile feeder insects, veggies and fruits. It even has a color coded chart of which should be used as staples, as treats or never