As F2P games go, FGO is fine. You can complete the entire story with free characters and tend to get a reasonable amount of free currency to get premium units.
The story is very good for a game of its type, while a slow starter the finale of part one was pretty epic and the characters are endearing. The story isn't very difficult but has its occasonal moments while the events typically have challenge quests to test your parties against.
As Welsper says, the international server is 2 years behind the JP server, meaning we can get a good idea whats coming up and plan to save in-game currency accordingly. Contrary to what Welsper says the JP game isn't ending any time soon with part three announced and its still usually the highest grossing game on mobile over there.
All in all you can do a lot worse than this as a mobile game, give it a go and see. If you do start let me know and Maz and I will friend you. The game has no PVP aspect but you can borrow one character from a friend to help out in difficult situations.