I wouldn't go with Athena/Tyr either, mainly because thunder is pretty unfriendly for a pure f2p. If you want to go with thunder, you really need at least either Kirin (100% eidolon) or thunder aphrodite (while she's still available) to make up the difference. Thunder is especially bad to start because you're going to have a hard time grabbing a flb Medjed if you're just starting now (and there won't be another decent one for a LONG time - you'd most likely have to buy one with eidolon orbs), and already missed the first thunder UE with flb weapons. So it'll also be hard to get a good grid together to make up for being a f2p. All in all, just a tough slog ahead, not recommended.

Looking at the schedule of events coming up, starting up with wind is still viable but difficult (need to get into a decent union asap), while fire is ideal (has time to start up, with typhoon reprint and wrath UE coming), while light and dark are decent because they get to doubledip on greed UEs.

/just my 2 cents