It really depends on your server, and the people in them. If you have whales that spend like crazy, then a lot! And if you started on a server that's pretty old, then it'll take awhile to catch-up and by then the strong players have already gotten stronger. If you start on a fresh server, you should have an easier time being completely F2P if you know what you're doing... like GNW, Ninetails, Sage-battlefield, frag-saving, etc. You can go Casual 2 Play, and spend like $6(?) dollars to get the daily coupon bonus for a month I think... You can then get the Jounin Medal and call it quits on paying and you should do fine.
So $6 dollars if you know what you're doing. The main cost that you will have is the time doing all of the crucial events to keep up or to surpass other players.