I bought a castle for 1m. Yep, I'm old.
So, back on topic, I've seen some actual one-of-a-kind items for sale for 1-2m. I know it's still more than the OP wanted to spend, but technically one-of-a-kind items are very, very, very rare -- even more so than the vine cords or whatever people spend their billions on.
See, the key is to actually *want* the odd/unusual 'rares' that are in fact very rare, for the rarity itself and not for the status others place on it. Then, you can collect affordably.