Heyo! Decent spender here. I would definitely advise going for one ninja with decent refines and leaving it at that, but even as P2P I would wait for refine event so since you are F2P absolutely wait.
The closest fights that ever happen to me are those of turn 2 dominance. Whoever gets that first big skill off turn 2 usually has a pretty nasty advantage in the next few rounds, sometimes even deciding the fight in that round alone. Even when someone is a few thousand BP below me I have learned to not count them out just because of how large that turn matters. However, you really only need that first ninja to be refined above others to get that chance. Hence, only buying and using refines on that one.
As someone mentioned it takes about 200 dollars to get to rank 4 battle armor at the moment because we have no way of getting medium threads. That being said just keep doing SA as it is and patiently increase that because the wall there isn't even kind to paying players and, quite literally, impossible for most people at the current time.
Magatama are another great investment but if you are already at all 3/4* I wouldn't advise that either. After that point it starts to take time to build them up naturally, even to 5*, so everyone usually slows down at that point.