On my first bicycle tour (I was a teenager in the '70s in Chicago) I'd never even heard the word "pannier." For your first tour, you can use gym bags, day packs, bungee cords--be creative. Some tourists make their own out of kitty litter buckets. If you like the activity, you can upgrade your gear as you go. Or just keep dirt-bagging it.
Start looking for end-of-season sales, used stuff on Craigslist and eBay, ask people you meet while touring, etc. If there's a bike co-op nearby, they may have a bin of used packs you can rummage through.