Magic Paths:
Picking the paths your pretender will have is always an important step in your pretender creation process. One thing you must shoot for as EA R'Lyeh is so important I'll bold it below:
You need to be able to make Amulets of the Fish!
Without these items, your Mind Lords and Aboleths cannot leave the seas. Air 1/ Water 1 is the minimum needed for these. This is a critical aspect of your pretender design. None of our national mages can make these, so that leaves summons, luck on sites, or your pretender. I always take at least air 1 on my pretender, and always take water (and astral as well) as default as any R'Lyeh.
EA R'Lyeh does not lend itself to a bless strategy. We only have the prophet and 3 national sacred units total. 1 of these nationals is aquatic and immobile (Polypal Mothers), 1 is aquatic and capital only (Gibodai), and the last is the Slave Priest. I do not build my pretender around any sort of bless capabilities, although I tend to go fairly deep into water and astral and get a small bless by default. But do not build your pretender based on any sort of bless strategy.
Air:
As previously stated, you want at least 1 air on your pretender. Amulets of the fish are just too critical to not do so. Most of the pretenders we can choose from come with water, so it's not hard to be able to at least make these items. Taking more air levels will let you make other nice toys like amulets of missile protection. I try for 2-4 depending on the type of pretender I am making.
Astral:
R'Lyeh is heavy with astral magic in all ages. Our national mages are heavy with it, and some of our pretenders start with it, or can get it cheap. The SC pretenders may skip astral as they need water 1 and air 1 to make the amulets, but for a more magic-orientated pretender, astral is a good fit. I try for at least 4 astral on my heavy magic pretenders. If you get Astral 6 or more, you can make the expensive but powerful Rings of Wizardry.
Blood:
An important aspect of blood magic is that you cannot blood hunt underwater. I do not normally take blood magic on my pretender, although in some longer games, I did empower them with it and had a small blood economy running. But that was more to test it out for EA R'Lyeh than anything else. You probably could take some on your pretender and try for some decently sized population land provinces to get a blood magic economy rolling, but it's difficult for EA R'Lyeh to use as our main strength is below the waves where we cannot get blood slaves. I do not recommend you get too much blood magic on your pretender, but a little bit can give you access to some of the astral+blood spells and items.
For an excellent article on Blood Hunting (and Mictlan of course!) See Baalz's guide here:
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Death:
Aboleths can have death 1 and Mind Lords can get up to death 2 (but that is quite rare as it requires the 100% pick to pick death and then get the 10% pick to give death as well). A little death on a pretender with many paths can certainly work well. I usually get some death, but not too deep into it. Death+water gives access to Streams from Hades which is a nice mixed magic summons, and also gives Hidden in Snow which is a rather good summons for us as they enhance our land forces. Death+astral gives the Ether Gate which is expensive, but I use them from time to time. All 3 of these spells only require 1 death magic, so even a a little death can give you some nice bonuses.
Earth:
Our various mages have some access to earth magic, and our home site makes 1 earth gem per turn. Earth magic gives the forge of the ancients and the dwarven hammers for cheaper magic items. Earth magic also gives some solid defensive and reinvigoration items with construction research. On a rainbow pretender, I try to get some earth.
Fire:
None of our national mages can get fire magic. Most fire spells don't even work underwater. If you are going for a rainbow pretender, fire magic can give you more items to choose from and some powerful spells for dealing with the surface dwellers, but it's not a priority for us normally.
Nature:
Only our Slave Mages can get nature from our national mages, and it's a random pick so not really common. I do tend to grab nature magic on my pretender along with water for the fact that I need nature magic (on top of water magic) to make Clam of Pearls. These items can really bolster your astral pearl economy and come highly recommended. Nature gives access to some nice reinvigoration and regeneration items and supply items as well. I try to take some on my pretenders whenever I can.
Water:
We live in the water, so taking some is an easy decision normally. Water works well with astral and you need water 1 (with air 1) to make amulets of the fish which we need badly. Water 3+ Nature 1 gives the pretender the ability to make clam of pearls too. Water 4 is my normal minimum as EA R'Lyeh, and I often take more.
Magic, Dominion, Wakefulness, Pretenders, and you:
A limited path SC pretender should shoot for air+water normally. You don't want to burn too many points on too many magic branches when the paths are costing you 40-50 each, but air and water access is critical. EA R'Lyeh needs a pretender with at least these 2 paths unless you want to gamble on finding air sites to empower or those rare indy mage sites, which I cannot recommend. Gambling can be fun, but if you don't get access to amulets of the fish, you can cripple yourself.
Awake SC pretenders have the advantage of aiding our expansion early, when we are somewhat weak. EA R'Lyeh is more of a late bloomer nation, but taking a low magic SC pretender hurts our magic item construction and magical capability as well.
On the other hand, magic-heavy pretenders (whether rainbow or simply deep into only a couple of paths), are not as effective early as the SC ones, but long-term they give us a lot of magical power in return.
Evilhomer recommends an SC for MA and LA R'Lyeh and this applies to EA R'Lyeh to a point as well, but I tend to take a Polypal Mother with heavy magic instead. If you get rushed in an MP game, you will want an SC, but if through geography or diplomacy you have some breathing room, a heavy magic pretender can work wonders in the longterm. The worst part of all this is that you won't really know which situation you will be in until you have already started the game!
The choice of an SC or a magic guru is largely personal choice. I tend to use my pretenders more for their ability to cast high path requirement spells than for expansion. I have tried both and an Ancient Kraken or Wyrm can really put some hurt on enemies. Which you prefer is up to your playstyle and the people you are playing against. SP games allow a lot more flexibility in pretender construction as the AI is not very 'threat aware' compared to other human players.
Awake, Dormant, or Imprisoned?
This is a very hard decision and I have to say that while I do not like waiting so long for my pretender to be usable, you get a ton of points with imprisoned, and a fair chunk if they are sleeping. If you take an SC, I would take awake for sure as early expansion is the main reason to have an SC. An immobile heavy magic type gives a nice amount of research early if awake, but you can eke out a lot of points if they are dormant or in jail.
As mentioned above, your decision here should be heavily influenced by the game you are playing and the personality of the other players. An awake SC may just be enough to keep that aggressive guy off you to let you build your strength, while having neighbors that are not so interested you lets you be a little more relaxed about this.
Dominion:
A very important part of god construction. Most of our choices here start fairly low, but it's a simple matter to bump it up. If you have really nasty scales, having a low dominion can let you sponge off other peoples better scales, but this makes you more vulnerable to being prayed out of existence. Taking a very high dominion can keep your scales in control and helps in the breeding of free Polypal Spawns. I try to get at least 5, and preferably more as I am pretty conservative on my scales so don't have too much damage from my own dominion. Getting 9 or 10 here can give an SC that extra edge with the Awe ability.
Pretender Summary:
EA R'Lyeh has very limited choices for our chasses, but we don't have any real problem ones like the Lord of Fertility either. Getting air 1+ water 1 is critical for us, but beyond that it's really up to your preferences. I always take water, astral, air, and nature on my heavy magic users. And dabble in the other paths most of the time.
Many of our pretenders can benefit from amulets of the fish to enter land based labs to cast land-only spells. A few of our pretenders do not need them to do so, and this increases their appeal. Pretender construction is an extremely interesting, critical, and fun part of the game.
I freely admit to a strong bias to the Polypal Queen. She just fits as the nation's goddess so well, and I like strong magic pretenders. The freespawns are a little extra. If they get out of control, I can always have her grab an amulet of the fish from the lab and port to a friendly land lab. This lets me halt freespawn production if it's getting too large and I can cast some of those land-only spells to boot.