I have a cat that is about 20 years old. She does not like Rosie at all.

I think she is too old to put up with a brat 3 year old yorkie. The biggest problem I have is making sure Rosie stays out of the cat food and litter box. She will also try to bully the cat. But I don't let the cat run loose so it works out for us. She is too old to be outside and she can't control her bladder to get to have free run of the house. This keeps them separate from each other.
As far as what to buy. Of course you will need dishes, cat food, litter box, and litter. I would buy toys because cats like to play. Also, I would get a scratching post or your furniture will be made into one. The only other thing I can think of is the hairball "stuff". I am not sure what to call it. But it keeps them from having hairballs. Even short hair cats need it. Good luck with the addition. Maybe if they are both young enough it will work out for you.