Crisis Core is certainly a member of the final fantasy lineage, though it plays more like a cousin of Kingdom Heats.
The fighting engine of this game is basically that of a turned based RPG that wants to feel like its in real time... remember Knights of the Old republic? There is a noticeable lag between when you push the X button and when Zack actually performs the desired action. At first this was a nuisance, but I got over and used to it quickly.
The whole game is pretty much broken up into missions... which makes the progression of story line feel like work. Since level-ups are decided randomly (BLECH!!) its hard to find the motivation to grind. Though you will find the strongest assortment of items and materia in the game by accomplishing side missions. Which are short enough to clear in a matter of minutes... perfect for the PSP!
Despite Crisis Core's short comings, I found it hard to put down until I was through it. For fans of Final Fantasy VII the Character Development alone will be enough drive to spend hours on end burning though this action RPG. The super polished graphics, amazingly produced cut scenes and along with excellent voice acting certainly won't hurt either.
In the end; Crisis Core is a worthy prequel... you will be able to pick it up causally, and play from beginning to end, grind free. You can also play every single mission. Unlock a ton of extra items and abilities and finish the game as a hulking mass of unstoppable, masculine, sword wielding, spiky haired, button mashing fury. Its your choice, enjoy.