I won a bunch of easterling troops on eBay for a good price, so i figured I should get some lists worked out. Here is what i plan to start with, but i'm up for making changes to optimise the list. I do like the idea of being entierly Eastrlings (or black dragons if they are worth it)

Warband 1
Amdur on armoured horse
6 Kataphrakts

Warband 2
Warpriest
4 Easterlings with Shields
8 easterlings with Shields and Pikes

Warband 3
Captain with Bow
11 easterlings with Bows

Total Units: 32
Break point: 16
Bows: 12
points: 501

I'm likely to face dwarves, wood elves and Minas Tirith, being over by 1 point doesn't tend to matter in friendly games, but if it does i can drop a pike.

I currently have no armies with cavalry, so i really want to use the kataphrakts, especially because the kit is awesome too!

First off, DO NOT give a captain a bow. Wasted points. 2- Id remove all the bows. when you move 5+ to hit and generally 6s to wound most models.....not good. You want your easterlings in combat anyway...

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It's handy to have some bows, but easterling archers are only average, so don't over do it. Don't be fooled by the 50% bow limit. This isn't anything to do with play style or background, just a rule change to make GW's poorly set up plastic kit more usable (comes with 4 shields, 2 pikes and shields, 4 bows)

You should never take more then 1/3 easterling archers, personally I'd probably only take 4-8 in a mono easterling army.

Finding the points for Black dragons is very helpful. You neither need, nor should go army wide, just in strategic locations. Fight 4 is handy enough, and when it is outmatched by elf armies, you still get the boost to courage.

Kataphracts really need this upgrade. At fight 3 without S4 or a lance they don't make great shock cavalry which undermines the hammer and anvil effect they are suppose to create (with the pikes). Having fight 4 and amdur's banner effect actually makes them a pretty decent shot at winning the fights, which goes a long way.

I share The Marshal thoughts, if you wanted shooting, khandish chariots would be far more decent on that job cause of full movement + shooting (despite being more expensive, althouh the survivability is greater and have advantage over charging other cav)

But anyway, easterling bowmen not exactly necessary, but you aint gonna give chances to oponents to shoot and run from you, so a couple bows just for psicological effect might do the trick.

About the rest, yes black dragons is a go, I would suggest as well upgrading the Kataphracts for it since they lack on punch, least they are more qualified (which means they compete vs gondor captains and cheap gondor heroes in equal terms)

Also would upgrade the front rank of easterlings with shield to black dragons probably, to have shielding option with better fight value and better chances to charge fear models, or the last rank to have fight 4 to win combat, since those will be the last ones to survive (and will justify the courage 4 upgrade as well)

As for other detail, maybe removing 3/4 bows and add horse to that captain and war priest, its gives em survivability and flexibility.

I think upgrading the Kathapracts is nearly necessery to make them win some fights and without winning fights you can't kill foes and instead get killed your Kathapracts.
Upgrading the last row of phalanx is a good idea, because you need to win fights there, too, because you are encircled, if you loose.

Compared to the good's bowmen with D5 the evil's aren't that steady because of the many S3 elve and dwarfbows.

I really like the look of Easterling Archers, and I have had success using orc bows against wood elves becuase of their shocking defence, but I will take the advice and drop to maybe 6-8 instead of a full warband.

Warband 1
Amdur, Horse
6 Black dragon Kataphrakts

warband 2
War Priest
4 Black Dragons, Shields
8 warriors, Pike Shield

Warband 3
Captain, Shield
8 Warriors, Bows

When i have more dollar to pick up more Kataphrakts to make a mounted captain, I might also grab a mounted priest. So hows this looking?

Thanks for all the advice so far!

I'd drop another four bowmen and have that captain lead a second shield wall or at least some shield guys. A four by three phalanx is just to small do much. Either make your cavalry big hitter by adding 2 or 3 more guys to it. While evening out your pike to shield ratio and use the infantry to support your horsemen. Or make your infantry a solid hammer and the horsemen can act as the hammer. As it stand now you have to few front line troops to do much. The Easterlings are not bad if you just run them like Gondor(regular shield wall) with the pikes as your ace in tuff fights. But if your what to try a phalanx you really should go with a bigger list 700 or 1000 points so you can get a respectably sized pike block together. In smaller games you might go with something like:

shaman
6 warriors shields
6 black dragons with pike and shield

Captain with shield
2 warriors shields
6 warriors pike and shield
4 warriors with bow

That would give you a nine by two front line with a captain on the front line. While the war priest and three pikes to move around supporting the supporters and using fury. I know that plus cavalry would run you over budget at five hundred points but its more of an example then a force suggestion.

One more thing be careful were you put the black dragon upgrade. If you upgrade your front rank guys they are going to die first and you could lose the advantage to shooting of a unlucky few combats. If you put them in back they might live a bit longer and they will pass the fight four to the guys they are supporting.

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