Are they completely random? Or is it after you've bought a certain amount you start getting the higher ones?

It's completely random. Buying the most expensive items or spending a certain amount of money won't guarentee you'll get a rare one. As Keith said in the most recent live chat, you're better off just buying them from other users because they're so rare that spending a fortune won't necessarily mean you'll get one :(

I was hoping that wasn't the answer. I don't have anywhere near the money to even get one

Once the new ones are released, the others will be retired and will be even more expensive to buy. If you want to complete your set it would be best to just buy them from other shops.