Off the top of my head Name, class, breeder or introducer, date (that part becomes tricky with different dates for breeding and introduction, and often different breeders and introducers; and then there are sports...)
Provenance is also tremendously useful and I would love that it become an accepted convention to include it in the essential information on a label. Provenance information is gold to anyone searching for answers to burning questions.
Personally, I also appreciate knowing whether the rose is growing on its own roots or on root stock and if so, which one.

Looking forward to what others have to say here.

In a public garden I would have 3 lines for Rose name / Breeder + Year / Class. The public is not interested in more information. We have one public garden which wants to add a QR-code, so that a story regarding the particular rose can be read/listened