The Kingdom of Wales is a Christian (formerly pagan) nation found on Great Britain.
The nobles of the area are the Cymry (Brotherhood) who joined Cunedda of Strathclyde in retaking the north coast from Irish invaders after Roman withdrawal left a power vacuum on the island. That Romano-Pictish kingdom — along with some more heavily Romanized successor states in the southeast — successfully resisted the Saxons, Black Gentiles (=Vikings), Barbarians (=Irish), more Saxons, and then the French (=Normans) for centuries until finally falling to Edward I, who filled Wales with England's greatest castles to hold it.
As so often happens with great storylines, the Welsh's greatest strength was their greatest weakness: their long history & many exemplars gave them purpose and drive. The king's bard was required — by law — to sing the History of the Britons before and after each battle and, while dreams of Cadwaladr and Cynan's return gave way to newer legends of Arthur, the Welsh never forgot the united Britain that once was. Unfortunately, that vision of union kept the Kings at Aberffraw in a perpetual funk about their fallen state, their countrymen in a perpetual revolt against any encroachments on their traditions and liberties, and everyone in acceptance that at the end of the day whoever was King in London was the rightful overlord of the island. (That acceptance, btw, is why the game calls the Welsh "dukes", the English historically called them "princes", and everyone else refers to them as "kings".)
While the Welsh ruled themselves, memories of past glory meant pedigree (within Wales) trumped genetics, alliances, or even wealth; foreigners had lower status than the serfs and could not nationalize themselves faster than 3 generations. Compassion among themselves also meant that the Cymry were constantly angering the church and horrifying the English by refusing to deny inheritance to their bastards. Most unhelpful from a game perspective — the title of high king at Aberffraw de facto passed by male primogeniture (assuming the eldest was of age and neither blind, deaf, lame, or mad) but the land of a family was held in common with all other sons of the same great-grandfather: at death, it was divided among the sons (including the bastards) equally, allowing them to build up independent power bases like Powys and Deheubarth and assert their de jure consanguinity rights to make a claim on the throne.
For added difficulty, the Welsh also typically kept their heirs at home in court (going out to establish a separate court risked invalidating the edling's claim) while the younger brothers were permitted to go establish themselves; marriage was avoided until after one's title and land were firmly established; and it was effectively forbidden to inherit below the age of majority around 28 — meaning if dad died any earlier than that, one was thrown into exile and plotting for how to retake the crown from the uncle or vassal who just took the throne.
Playing as the Kingdom of Wales:
In AD 1066, the titles of Wales are divided among the Kingdom of England (Cornwall and Devon), the Brenin of Gwynedd (Gwynedd and Powys), Gwynedd's vassal (Perfeddwlad), the Brenin of Dyfed, and the independent but petty lords of Glamorgan and Gwent. The current lord of Gwynedd is a Saxon usurper installed by Tostig's massive invasion just three years earlier; the rightful lord is an exiled kid named Gruffydd in the court of Dublin; and the other three are barely holding on.
Given that England is simply much stronger than any of the other claimants, the three ways to go:
(i) Historically, the lords of Wales would pledge fealty or accept vassalization to England any time they needed to. Five minutes after the Norman army was on the other side of Offa's Dyke, they'd fall back into their local feuds with each other and the Marcher Lords. In-game, you could join whoever wins in England — possibly building close ties through fosterhood and marriage — and use the English army to smash your rivals within Wales, while slowly making yourself powerful enough to survive your future bid for independence (England's crown authority will probably be low enough to allow wars within the realm, permitting the recovery of Chester and Hereford as well as Cornwall). If the king or other lords grab your sieges first, however, it might become very difficult to pry them free again.
Pledging to Scotland or working with English revolters is much riskier over the long run.
(ii) Less realistically but probably better within the game, you can instead take advantage of England's distraction to smash your rivals and establish the kingdom quickly, hopefully overrunning Ireland as well before any Saxons, Frenchies, or Vikings come looking for you. (Scotland is more of an outside chance.)
Bleddyn is a miserible usurper but he's in the best position right now (and for what it's worth was remembered as a "good king"), so going with him, build your claims on the south as quickly as possible. Upgrading to castle towns will help improve your poor income. Similarly, avoid handing out titles except to strengthen your heir just before inheritance since you'll need the money.
(iii) Give up on living anywhere near London and recreate the exploits of your ancestor Cunedda by loading up into ships and heading for the Baltic shore or Promised Land. (Although, honestly, if you wanted to play in that neighborhood, there are other states you could start with instead...)