Here I am, as requested
I am more a specialist of the early post-Roman period (5-7th century) than the later one (9-10th) but I hope this will help.
As suggested I think a Brittonic faction may be better suited than simply Welsh. You can call them Britons, they will encompass various Welsh kingdoms, Cornwall and Strathclyde which was a major power in Scotland up to the 11th century.
Emphasis won't be on archery. That's likely a later, high medieval development of Welsh warfare against the Anglo-Normans of the 12th and 13th centuries. In the early medieval period it is unclear if Welsh used a lot of archers, at least it is not depicted on stone carvings and not much quoted in textual sources.
Light infantry and skirmishers are a good guess. Welsh and Bretons were masters of guerilla warfare. Warriors with small round shields, javelins and spears, good both at range and when closing orders. Few or no armor.
Heavier infantry would be good, although they would be less heavy than Saxons or Viking counterparts. Some with helmets, other with larger shields, spears, swords and other melee weapons, but they can also get a few javelins to throw before melee fight.
Cavalry, both light and heavy. Light cavalry would have javelins, spears, swords, no or few armor, some with helmets, small round shields.
Heavy cavalry would be elite and bodyguards, the
teulu, litteraly "family". They would have the best equipment avalaible, including mail and helmets. Otherwise swords, spears, roundshields, javelins. They would also be great to dismount to join the shieldwall (or you can do an infantry unit with similar equipment).
As for their look, go for long knee-lenght tunics, or shorter ones with knee lenght trousers. Cloaks are important and in battle they can be worn across the body for better protection. You can give some of them checkered patterns for a regional touch, but make sure not all garnments are checkered as that would be much of a cliché.
Saxon and frankish swords were used and imported. Helmets can also have cheekguards but would otherwise be quite similar to saxon helmets.
No more "roman conservatism" by then so if we can accept late roman styled helmets for late 5th-7th century Britons it is not true for 9-10th century ones.
There is a really good 10-11th century re-enactment group in North Wales, Cwmwd Ial. You can check photos of them here:
http://www.flickr.com/photos/bledri/3209818091/
http://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&ved=0CD4QFjAC&url=http%3A%2F%2Fwww.facebook.com%2Fpages%2FCwmwd-Ial-Inc%2F105023746205069&ei=cxu2UNirLvGT0QXqjoD4BQ&usg=AFQjCNFKlAkAchCLmaC8M63lwDbyf8OdEA
http://www.myspace.com/rhagner/photos/1097576