Right, so there's a couple of different answers to the question "Can I play against a faction from another book?".
The short answer is yes, any historical books can pretty much play against each other. Age of Magic is probably best left as its own thing.
In my experience the imbalance is not really between Ages but just that some factions are a bit stronger than others.
The slightly longer answers is that Studio Tomahawk stated recently that their intention is three eras that they think are balanced internally, being Antiquity (Alexander, Hannibal and the upcoming Caesar), Early Medieval (Invasions and Vikings) and Late Medieval (Crusades and the upcoming Chivalry). Different groups and tournaments vary how they pair factions together, but for casual play my opinion is it's better to just have people play the faction they are exited by and have more opponents.
As for your Welsh, I reckon the vanilla Welsh seem the strongest unless you really want to play with the AoI mercenaries. They have so much more flexibility with equipment options. I would rate Alt Clut second as mounted javelin welsh is a strong build, but hampered by terrain, so you are less flexible in your deployment then the regular faction. Cymry seem counter to what the battleboard really wants you to d, so very situational.