I think of the PFF as Disney Princess Russian Roulette because you never know who will be there. And if you only care about seeing a specific princess, it can be a real pain. I once overheard a family who was waiting in line for the royal walk for the 5th time because the daughter had to see Cinderella. Not even Ariel's Grotto had helped them in that quest. Suffice it to say there was a very excited little girl and very relieved parents when the dad came back to report that he saw a pink dress, a yellow dress, and a blue dress.
The coronation is a roughly 20 minute show where the children learn royal manners and a very simple dance that they show off to the 3 princesses who come to visit. Near the end, there are 3 maypoles and everybody who wants to grabs a ribbon and runs around the maypole with one of the princesses. I would describe the show as cute for the kids, but potentially over the top cheesy for adults. That said, it can be an excellent way to meet 3 princesses (or just one) without standing in the long line to play Disney Princess Russian Roulette. Be aware that all 3 princesses will not be out for the same amount of time, so choose wisely. And if one of the 3 is going to do storytelling, her time will be shorter than the others. I have seen CMs cut the line off and turn guests away because of that.
Hopefully, but not guaranteed, the 3 princesses come out 5-10 minutes after the show ends for meet and greets. The same 3 in the show will be the same 3 that come out, if they do, for a meet and greet. A lot of people leave right after the show ends, so make sure to stick around if an individual photo/autograph/et all is desired as there is no chance whatsoever to get an autograph and/or nice photo during the show. If you're lucky, a CM will tell you the best way to meet a certain princess if one is more important than the others.
The storytelling is cool. One princess comes out and tells her story to the audience. One lucky little boy (or maybe even older boy) will get to play the part of the prince and dance with the princess. The CMs may not tell you which princess is doing the storytelling. There is no individual meet and greet opportunity and the only guest who will get his picture taken with the princess is the prince during his dance with the princess. When the story is over, the princess will leave. I'd say it's worth seeing if you have one who just wants to experience this or you know that a favorite princess will be telling her story. Just be aware that there will be no meet and greet if that is a must.
As for Rapunzel, I've heard that people start lining up in the queue 30 minutes before the first meet and greet time. You may also want to try 15-30 minutes before the start of the parade as the parade does a nice job of swallowing up the crowds and may lessen your wait somewhat.