I think I said that right. I've yet to figure out how the system works- I've tried a variety of items with not a crystal to my name. Am I missing something?

The higher the rarity, the more likely you are to get a crystal. If you toss a bunch of very common items in, you will eventually get a crystal through pure chance.

Thanks! Wow, this might take a while, I wanted that new blade they're offering but looks like I'm going to need a LOT of items if I'm gonna get it!

Generally, I've found it easiest to find a relatively cheap 'Rare' item or above, and buy as many as possible. Then go and frag them.