The top 4 are
Palp
Tarkin
Padmé
JKA
Any order is fine for them. Tarkin helps in Fleets as well and is generally your first Fleet Commander, especially when running Geos (I was actually surprised to see your Geos running under Ackbar), so that helps him rank high. Palpatine 's zeta is a completely transformative one for the entire Empire faction (and a good number of Sith function well under it, too). So, of course, he's way up there. Padmé requires 2 zetas to really transform the GR, but when she gets them, it's as big a deal as Palp's lead. The downside is double the zeta cost, but the up side is that you actually have enough GR toons to put together in a full squad at good gear. It might cost twice the zeta mats to transform the GR faction, but you actually have a pretty beefy GR faction right now, while your Empire faction might do a lot better, but they're in such poor shape that transforming them from pitiful into average may not help you as much as GR transforming from mediocre to very good - certainly good enough to get a fair number of Conquest wins.
JKA, of course, has Jedi synergy, GR synergy, and a great ship, so with his multiple uses he's worth the gear even if he's not a transformative leader. So, yeah, you can do the gear in any order that seems best for you, but all 4 can help a ton in Conquest and just generally. (Tarkin won't help in conquest much until you get Palp's lead zeta, but he helps your fleet in the meantime.)
Next few toons?
Kanan & Thrawn for pure gear
Bastila, Ezra & Old Ben for gear + shards
When you can, get MagmaTrooper to 7 stars. You don't have to gear him, but he's a GW store farm, which means he's incredibly quick. It takes just 11 days to max him out from nothing (and you already have him unlocked, so maybe a day less than that).
With Palp's zeta, Vader can basically solo the R2 event, but you have to have 5x 5* Empire toons to unlock and 5x 7* Empire toons to get R2 at 7*. All you have to do is bring Magma to 5* (about 4-5 days from whenever you start) and you can unlock R2 and start giving him gear.
In the meantime if you get Ben to 7*, you can have CLS quite quickly, and then your CLS faction will also be of use in Conquest.
So, big question: have you got zeta mats on farm yet? It looks like you should already have the zeta challenge beaten & 3-starred. If that's the case, I would temporarily switch GW purchases to this:
- Minimum 2000 GW tokens in the bank to purchase Sun Fac's ship ONLY. Never dip below 2000 unless it's to buy Sun Fac's Starfighter.
- Magmatrooper with anything over 2k shards.
You should have R2 unlocked in 5-7 days. In 15 days or less you should have Magma up to 7* and just waiting for one more empire toon (possibly Thrawn) to boost r2 to 6 and then 7 stars.
Then transition back to this:
- Minimum 2000 GW tokens in the bank to purchase Sun Fac's ship ONLY. Never dip below 2000 unless it's to buy Sun Fac's Starfighter.
- Anything over 2k:
Imperial TIE Fighter
Geonosian Spy's ship
Geonosian Soldier's Ship
When you're running short of currency, make sure you do those last 3 ships in that priority until all of them hit 7*.
Imp TIE is a rare ship in the GW store, but you don't want to use more important currencies to buy it elsewhere when you could buy it there with just a little planning ahead.
It looks like you're getting discouraged with the rarity of certain farms & thus deciding not to bother (this is what I concluded from looking at how poorly you're doing picking up Sun Fac blueprints). But the truth is that if things are rare, that means you have to prioritize them MORE highly just to make sure you have currency available for them when they show up.
Now, Imp TIE is not a more important priority than Geo Spy & Geo Soldier's ships are for you, but once the Geo Starfighters hit 7-stars, then Imp TIE should go even higher on your priority list since you'll be using Tarkin's Executrix. Of course, you can't go higher than 2nd, but what you can do is this:
Keep a bank of 3,000 GW tokens.
Never go below 3,000 for anything other than Imp TIE or Sun Fac's ship.
Never go below 2,000 for anything other than Sun Fac's ship
Anything over 3,000 tokens you can spend on your next GW purchases.
We can talk about what those priorities should be if you haven't already got a plan for that, but you won't need them for several weeks yet since just Magma is going to take a couple weeks and then finishing the 2 easy Geo Starfighters will take a couple weeks more.