Unless you plan to reroll alt accounts until you have the perfect team or willing to spend a lot of cash, you likely won't be getting a proper full single elemental team any soon.
Right now, the free units from story you get are:
Diabolos - SR Dark Eidolon
Nike - SR Water Kamihime
Amon - SR Fire Kamihime
Cybele - SR Wind Kamihime
Baal - SR Lightning Kamihime
The 2nd and 3rd zone provide a lot of Wind and Lightning element stuff and farmable items to exchange for a SR Eidolon and weapon. You can get Fire stuff from the 1st zone but no exchangeable unit or weapon. You do get a SR Fire Eidolon for doing the beginner panel but most likely won't be able to limit break it.
According to JP wiki, regular gacha should only have 2 R Kamihimes of each elemental, nothing above R. (Correct me if I'm wrong, since you can't check contents of regular gacha in-game.)
A Dark team would probably be the most suited towards end game from what I've heard and the first event unit should be a Dark Eidolon too, which shouldn't be for a while I assume.
So from the looks of it, most difficult to obtain to easiest, as of right now, would probably be something like: Light > Water > Dark > Fire > Lightning = Wind.
A mixture of element while slowly building up on a single kind is probably ideal right now for free players. Of course who you got from pre-register or the 3000 jewels from tutorial may play a part in deciding.
Though if you're willing to whale this early then everything I mentioned is irrelevant.