It really depends on your preference. Personally, I am f2p and I still enjoy the aspects of the game, if anything being f2p forces you to be more creative and innovative with how you play and spend coupons. Others may like spending money to get ninjas or items faster, but eventually you'll get the same items if you play regularly, just takes longer.

As for events, Lucky Board is the best event for starting servers. I'm not sure about the ingot events though, but I suggest you invest your ingots in Monthly card and other high-return rebate deals.

Dude if you don't have a job right now why would you put your savings on a browser game? o_O

As for your other question, cheapest events for power would be Lucky Board (random stuffs), Treasure of the Sage (refine runes, cave key packs, myouboku packs). For ninja frags it depends, Jounin Minato and Masked Man currently have a 40% discount in Treasure of the Sage. Mission Mobilization gives you a good amount of redeemable frags without even putting ingots on it. Fateful Choice rates depend on how lucky you are in the points it gives you.

But seriously dude, savings on a browser game? When you don't have a job currently? My advice, just get the monthly card and be content with that.

Recharging on new servers is the worst way to go. I mean seriously do you want to be top player on a dead server? If you're going to recharge, go to an older server, like somewhere in S1 to S20 at the minimum. You'll get more out of it.