Congrats on getting the CBs, they are one of my favorites. I feed a good finch mix, Hagen's VME Finch Staple. It is not generally available in my area, but my bird club does a group order. Any finch mix from any of the good companies will work.
You'll just have to try veggies with your birds to see what they like. I follow Doug Taylor's Green Day diet--
www.gulfcoastfinches.com. So my birds are getting a mix of broccoli, cabbage, and carrots. But from time to time, I offer other things, and sometimes I am out of one of the veggies. Sometimes I just have broccoli. Birds are all individuals, so they don't all like the same thing--some will eat corn, peas, cucumber, etc.
The eggfood I use is from Doug Taylor's diet. I do make mine drier, for some reason my birds seem to like it that way, and I figure the closer it is to dry commercial eggfood, the easier it will be to leave them for a few days with the dry stuff.
There is a whole section on nutrition at the Finch Information Center, linked at left. Also, if you do a search on here for eggfood, you will see that there are many different ways to make and offer this to your birds.
Your CBs will love mealworms, but don't give them too many unless they are feeding babies. 1/2" should be a good size--if they are too big, they won't fool with them.
Good luck with them, and welcome to the forum!