>>47812215i did a monotype run of x and y at one point and made some notes on available types. You have to be aware that there is a serious lack of specific types until very late in the game. Rock, ice, dragon, ghost, and steel are super rare. But water, flying, normal, and bug are super common.
If you really want a rare type, you could always do a duotype nuzlocke, where you have a rare type and a common type. Something like Water/ice is a cool combo i think.