I'd choose neons over cherry barbs for a 10 gallon because they stay smaller. If you want cories, I'd suggest c. habrosus, pygmaeus, or panda. All stay small. You could keep 4-5 neons and 3-4 small cories.
What about upping your corys to 3? The do better in schools. The pandas are sssooo cute. Yeah, neons are probably better for a 10 gallon, but gosh, those cherry barbs are just precious. My neons really like to be in groups of at least 5, so that would probably stock you.
I'd choose neons over cherry barbs for a 10 gallon because they stay smaller. If you want cories, I'd suggest c. habrosus, pygmaeus, or panda. All stay small. You could keep 4-5 neons and 3-4 small cories.
I forgot to add that you'll need to stock slowly even after your tank cycles. I'd start with the neons... cories can be even more sensitive in newly-established tanks IMO.