Despite the name, Final Fantasy XIII-2 is quite open to new and old players. It includes a very good Beginners Guide in-game and explains mechanics well so it can definitely be a starting point for players new to the franchise.
Game play-wise it continues the battle system of Final Fantasy XIII where the player controls one character and the other two are controlled by AI. For the controlled character the player can either manually input abilities or allow the computer to automatically input abilities which can be vital due to battle being very quick or even during longer battles where the time taken to input commands can be the difference between life or death. The battle is still ranked on a 5 Star basis with clearly explained rewards for getting a 5 star rating (due to completing the battle quickly). Changes to the battle system from XIII include better AI (where they will now be more effective from the start even if all the information on the enemy has not yet been deduced on an enemy) as well as only having two playable characters to choose from: Serah or Noel. As well as the option of the third character to be captured monsters to put in the party, so throughout the game the battle system never seems to stagnate as you meet new enemies and gain new party members to choose from for a third part member. Plus the playable characters can be any class so the player gets more control in battle.
The story takes place after the events of FF XIII focusing on these two main characters: Serah, the sister of FF XIII's lead character Lightning and the fiancee of the hot-blooded Snow Villiers of XIII, and Noel, a new character of mysterious origins who pulls Serah into a fight spanning through time to bring back Lightning who seems to have gone missing after the events of Final Fantasy XIII and stop XIII-2's villain Caius.
Since the game takes place through time, the player can go to different destinations through the Historia Crux allowing the player to choose which place they wish to go. However the choice here is actually quite limited as there is only really one main branch during the main story (which in the end both have to be completed to continue the story anyway) with most of the others being side quests. Due to this, completing this game to the normal ending is rather quick for a Final Fantasy title, but there is a lot to do in this game other than the main story, with many destinations on the History Crux map not required to visit to finish the main game. Plus, there are alternate endings to see as well as a secret ending to see after completing every side quest and destination.
Story-wise the game is quite strong however not as strong as previous entries to the series. Quite a lot of the characters are one-dimensional and some can even be quite annoying. On the other hand, the main characters do grow quite a lot during the game and the story overall is quite engaging with generally good pacing on when the game answers questions, has serious moments and when it has silly side quests (however due to there being the option to leave a level and go to another one at any time, a disconnect can occur between the perceived importance of a story sequence and the players ability to go and spend time playing mini-games). Plus, the main villain has quite a lot of depth in the end with him actually seeming the most human of anyone of the cast, and since most of the filler is left out into optional side quests, the game is generally quite engaging throughout giving quite a worthwhile experience even if you choose to ignore all the side content.
Final Fantasy XIII-2 has a high level of polish and is consistent throughout. There is a lot of content and a generally good story.