Yay, Franniee!!!
TCO has great advice. I HAVE found a few stones that I would have loved to tumble, only to find them too large for my smaller barrel.
I ran out of grit awhile back and need to order more. but I remain undaunted. I threw a handful of sand in there to make do for now...
You can find rocks anywhere, and you'll be surprised what a "regular old rock" can turn out to be. I found agate, bloodstone, and jasper in my driveway, and wherever I go, I'm always on the lookout for stones on the ground that look like they might be something pretty. I also (shamelessly)began asking all of my train trade partners if they'd pick a small stone up from the ground near their home and stick in the the envelope with my deck...
Online, google "rough rocks for tumbling", "rough stone for tumbling", "lapidary scrap", etc.