Hm. Yeh, on second thoughts (now I am fully awake), natural armour might be a bit bleh, or broken, not even sure what's worse.
More to the point, giving one of the other could be preferable to giving both.
So, more DR. . . and/or increased DR during Rage / Berserk / whatever it's to be called (!) . . .
You know, I think doubling it during Rage might be OK after all. You might want to disallow things like Extra Rage and suchlike, though. Dunno, could get out of hand, is all. Then again, berserking is (obviously!) such a focal point of their whole schtick kinda thing, I'm undecided on that.
If they are
strongly tied to their 'sky god' (Odin, say) - or even a slightly similar figure - I can see a small amount of the appropriate Resistances (GM's discretion applies here, of course) being fine, too. Perhaps where natural armour was in that progression? For some unholy reason, Fire and Ice suggests itself as a label for that gift, until something better comes along (I pray).
Er, before I go rambling further, is any of this good. . . bad. . . ugly?

Eh, nevermind. I'm in a rambling mood anyway. Besides which, I didn't get very far there.
What about some rituals (other than berserk/frenzy/rage? Maybe something that takes time, perhaps a skill check, even a small personal sacrifice of some kind? How does this sound for an alternative to douibling DR during Rage? Maybe there's an entirely separate ritual they can perform that doubles their DR temporarily, perhaps with a small drawback for a time afterwards? That way, Rage might be less 'broken' in terms of providing *all* things that they require, and it would allow full access to the various Rage-related abilities and feats etc., without the system suffering at all.
Hrm, come to think of it, there are other ways the class could be pushed, or nudged, that unfortunately would step all over the toes of your PrC's. Otherwise, they could be good.
Is the plan to use this as the base, and the PrC's as optional paths of specialisation and increased investment in their religion? Again, nevermind: I looked it up.
So, all in all, this base class should be primarily a straight warrior (barbarian-style) type, I take it. I wonder if there's a good way of 'foreshadowing' though. . . that is, hinting at elements of the PrC's without actually granting any of them to the Berserker. Minor aspects of wolf and/or bear, that kind of thing. While they might grant some small benefits to the PC, they could also add somewhat to the 'flavour'.
FUrther note: I think it should be wolf
or bear, not "and/or", if you decide to use that idea. A berserker could decide (or have it decreed) right at the start (0 or 1st level) whether they are of Wolf or of Bear. That would then, of course, dictate the viable option of PrC between your two. As well as what skins they're wearing, for all that might or might not matter per se.