It's a common misconception that cories must be kept in groups... they do not.
Weekly water changes are best, no matter your stocking levels and tank size, so don't let that factor into your decision.
Your 10 gallon will be just fine w/ a school of 6 neons, and 3 or 4 dwarf cories, and your betta! None of these fish get huge, and they are all low waste producers. Again, this all hinges on religious weekly water changes.