So, I never actually went with Palp's lead zeta, but my shard (June 18) was dominated by them until zBastila teams took over. You'll get a lot of mileage from it, especially since your shardmates wouldn't have gotten her as a marquee.
Have you unlocked the T3 Ship Ability Mats Challenge? If not, that should be your fleet currency priority -- building your fleet up to the point you can at least 3* that so you have a shot at zetas from it. Without it, zeta abilities will still be a ways away for you. I sank currency into zeta mats directly before having it on farm and that set me back a fair amount.
Regarding omegas, they are absolutely still very important, although usually less impactful than zetas. For you, I would zeta EP's lead once you're able to. In the mean time, I would run EP (L), Vader, Tarkin, TFP, and Thrawn once he's unlocked. I would omega Thrawn's specials first probably since each has its cooldown reduced by one, which is huge. Then I'd do all of Vader's, they're all really good. Then go back and do Thrawn's basic. Then EP's basic and first special, TFP's TIE Strike, and then if you want to stick with this roster I'd do Tarkin's omegas. They're good, with Special 1 being the best in most situations. Special 2 is only rather important if you use him on a team without EP lead. Basic is good for assault battles and TBs and the like since the stacking potency carries between rounds, but in arena and TW you won't notice a whole lot of difference.
E: regarding further zetas, I agree with @komji15. Farm Nihilus and Sion once you unlock their nodes, and once they're geared up well and around 4* you should swap them for TFP and GMT. Sion's zeta is a must then. Then Thrawn's Ebb & Flow, then go on to another team as none of the other zetas are useful enough to do unless can afford a luxury zeta.
