Starting a D&D group can get expensive with all the books needed for game play. Wizards of the Coast has educators covered with their Educators Kit and D&D Beyond Educators License. Click here to reach out to them and put in your request.
There is always theatre of the mind, but in my experience kids like a visual reference to help them pay. Minis and terrain can get expensive, but there are inexpensive work arounds.
Study after study has found that role playing games foster kids social skills, creativity, and emotional development. Check out the research that spotlights the benefits of TTRPGS for kids.