Personally, unless you've studied pedigrees and really know your standard and the persians are tested, then you really should not just go out and buy a male cat.
I would try and show her, contact a breeder you can work with and let them breed her for a 1st time. Take your time and learn as much as you can before you just put 2 cats together. Just because they come from show lines, doesn't mean they are show themselves.
I would take her to a few shows and see what judges and other persian breeders have before I'd do anything with her.
Also can you post a few pics of your cat (head, body, front and side views). Some of us in here can advise you on the quality