I would vote in favor of C++, for a number of reasons.
First of all, C++ has quite a bit more that's reasonably similar to Java, so the transition is likely to go a lot more smoothly. This is even more true of the library than the language itself -- the Java library is much larger than either the C or C++ library, but the C++ library has enough more that it won't be nearly as foreign. If you decide to go to C, plan on feeling utterly lost for the first few months (at least) simply because the library provides so little of what you're accustomed to being able to use. You'll probably still feel like you're missing quite enough with the C++ library.
Second, in terms of concepts, C is nearly a subset of Java -- essentially the only thing it has that Java doesn't is pointer arithmetic, which I've never seen as being all that big of a deal. Although Java has generics, you'll quickly find that C++ templates really have quite a bit that's new, different and (at last potentially) quite interesting. With C, you're not really likely to learn a lot that's new or different (other than, perhaps, a rather different (minimalist) viewpoint on programming). C++ has a fair number of new and different concepts to learn that simply aren't present in either C or Java (e.g., template meta-programming).
C does have a couple areas where it's virtually the only choice. If you want to write code for really tiny microcontrollers or operating system kernels, then yes, there's a good chance that it's what you should learn. Though it's only personal opinion, I would say that in most other areas, C probably should have been dropped a long time ago, and continues to be used primarily out of momentum (we've got 7 zillion lines of C, and we're not going to rewrite it...) or simple bigotry (e.g., see Linus Torvalds's rants).
As far as Objective C goes, the situation is fairly simple: if you're going to write for an Apple system (MacOS or iOS), everything else is clearly and definitely relegated to secondary status. Apple does their best to push the idea that all development most be done in Objective C. While it's possible to do otherwise, Apple is pretty clearly doing their best to make your life as difficult as possible if you insist on doing it.
At the same time, total use of Objective C on all other platforms is probably easier to measure in parts per million than percentages. For most practical purposes, "do you want to learn Objective C?" can be rephrased as "do you want to write native apps on Apple machines?" with essentially no loss or change in meaning.
Bottom line: C and objective C both have strong niches; if you're interested in one of those niches, you virtually need to learn the language that fits. Otherwise, I'd have a lot of difficulty recommending either one.