My Eldar are all painted and themed. They hail from Craftworld Ulthwe. As such I always use a Farseer, possibly two, and a large council of warlocks as well as lots of Guardians. Ulthwe is noted for its Seer Council and of course everybody's favorite special character Eldrad Ulthran.
The Farseer is really the capstone of an Eldar army themed or not. They are very formidable opponents especially with a retinue of warlocks. They bring to bear psychic powers that help your units and hinder the enemy. This is very different from the powers that most armies have. Most armies have all attack powers with a couple that may enhance or protect. Eldar powers, especially warlock powers, enhance and protect your units. The actual attack powers are very good. Mind War has fallen many troopers and enemy commanders. Eldritch storm is a nice one for lightly armored targets with the bonus of flipping vehicles around. Destructor, for the warlocks in the retinue, is a nice one for thinning out light infantry. Combine the psychic powers with the ability to cast multiple powers and make your opponents roll psychic tests on 3d6, thanks to Runes of Warding, and you have psychic dominance of the table. I prefer the blanket effect Runes of Warding has to psychic hoods, not to mention they cover the whole table. An entire unit with an invulnerable save and weapons that wound on a 2+ is also very nice against, well everybody. Most people do not expect your HQ to be a lethal tank killer either. Since Singing Spears and Witch Blades count as strength 9 versus vehicles it makes for a nice surprise when you pop them out near the tanks and let them tear them open.
Sometimes I don't run two seers, but my first choice is always a Farseer as my primary HQ. If you have a lot of units being held in reserve an Autarch is a good choice if you want to get them in quick. You can stick him with different Aspect warrior squads with a nice mix of war gear from several of the Aspects. In most cases the Exarch powers with affect him. I use an Autarch with Swooping hawk wings and deep strike him with a unit of Hawks. This still allows use of his Master Strategist rule and its always nice to deep strike into the rear of a tank or artillery unit with a fusion gun.
I take the Avatar as a second choice when I need some heavy hitting. Since I like to use lots of Guardians, it is great to put him in between my two squads. Since he makes all units within 12 inches fearless I have a huge mass of troops that will not run and will continue to march forward until they are within catapult range. A squad of 15 or more Guardians laying into a squad or an individual is not pretty. My Guardians have fallen Trygons, Daemon Princes and even greater daemons from sheer weight of fire. It also Helps to have the Avatar there for any cleanup work.
I do not use Phoenix Lords a lot. I do have a themed infiltrator / deep striker list that uses Karandras with an Autarch as a secondary HQ and 30 striking scorpions, but other than that I do not run them that often. Although expensive they are worth every point. They make an Aspect Squad of the appropriate shrine very deadly. It would be nice if they did not take up and HQ slot and were an uber upgrade for the Aspect squad. With only 2 HQ slots its hard to pick one of them. This is why I tend to use them when I have a themed list. Karandras in the list above is one example. I use Maugan Ra with my Ulthwe army as a point of fluff. Since the Dark Reaper Aspect is the most populace on Ulthwe I like to use Dark Reapers a lot. Maugan Ra is always present in Apocalypse games.
So there you have it. The HQ choices and my two cents about them. I like themes. I have always believed the HQ slot to really set the theme of an army. Be it an Avatar and Phoenix lord lead army from Biel-Tan, to a Seer heavy army of Ulthwe. So next time we will have some battle reports from the campaign I am playing in at Evolution games that starts today and the army lists and possibly the results from the third round of the GW store tournament series that is this Saturday.
Blood Runs, Anger Rises, Death Wakes, War Calls!!!!!!!!!!!!