It's important to keep in mind that a 100% eidolon gives you access to 2 strong eidolons, not just one. You'll have your pick of friend eidolons, meaning it's easy to run 2x +100% eidolons or pick up another element down the road. Alt accounts with +100% eidolons are not as useful as you'd think since the account has to be active to show up as a choice when you're picking friend eidolons, and you only get to choose the same account 2x in a row.
If you don't want to spend much, Thunder is not a great choice due to the poor lineup of SRs and Rs. Dark is pretty good, especially if you don't want to work on a second element since it has no elemental weakness. If there's another element you'd like for its playstyle, that's fine too. I think Wind is a particularly good choice since Hraesvelgr brings such a powerful debuff.