Is it just matching barbarians you want, or wider fantasy ranges? If the latter, there are plenty of ranges that scale well with the Copplestone barbarians. I've attached a photo that shows a Copplestone warrior with Essex orcs and a dwarf, a Blood Dawn "great orc" (from Magister Militum) in the background and some goblins (also from MM, again from the Blood Dawn range, I think). They all work well together.
The Chariot range from Magister Militum is a bit on the small side: true 15s - although that doesn't matter for orcs, etc. But I imagine their humans would look short and weedy next to the Copplestone chaps.
As for rules, I'd second nic-e on Dragon Rampant but also recommend Hordes of the Things (HOTT). It's a superbly balanced set of rules that has only required a single rule change in the 25+years of its existence, despite being popular throughout. Most people play it in 15mm I think (I don't know why, to be honest, as it doesn't require much space or lead to play in 28mm). Anyway, it's a great massed-battle ruleset - one of those "easy to learn, lifetime to master" games - and its basing can be used for Dragon Rampant (which is really a "large skirmish" game) and other good massed-battle rules such as Mayhem, Rally Round The King and (from what I hear: my rules are in the post) Sword and Spear.
Basing is really the key thing here. If I were starting in 15mm, I'd base most (80%) miniatures to HOTT/DBA requirements, as that's the nearest thing to a universal standard. It's 40mm frontages, I think. Then I'd put the remainder on individual bases. That allows casualty removal in Dragon Rampant and gives you individual heroes and leaders for Mayhem and (I think) Sword and Spear. And the individuals also give you a skirmish force into the bargain (for Song of Blades and Heroes or whatever).
As an aside, I think you can trace the DNA of HOTT in both Dragon Rampant and Song of Blades - which is no slight on either. They're all great games with some slight common ancestry (I think). The three of them cover massed battles, large skirmishes and small skirmishes quite nicely.