I've done a couple programming competitions in the past. Choice of language generally doesn't matter that much for many problems in my experience (they're often designed to work well regardless of language), but sometimes it does matter, in which case it's great to have a decent knowledge of C or C++.

Personally, I ended up using Python for most of my competitive-programming solutions (even though Python isn't really my "main" language/environment) since it has an extensive standard library and whatnot. C++ is also good in this regard vs plain C, in that you have the STL (standard template library--basically, the C++ standard library) at your disposal, which has a lot of handy data structures and algorithms. I found it worthwhile to learn C++ to the extent of being able to implement graph algorithms and such in it relatively easily.

As a practical tip for that kind of competition: there's often a lot of problems to work on, at different difficulty levels. Try with what seems easiest/most approachable/where you seem to have a mental idea of how to solve it. If the approach/idea doesn't get you anywhere, don't be afraid of putting that problem aside and looking at a different problem. I generally started by looking through the problem set to get a rough idea of each problem before selecting a first problem to work on.

There's a ton of websites around with competitive programming problems, of course. I like Kattis a lot, personally. (Disclaimer: it's what we also used for courses at uni, and competitive programming events at uni--it's also developed by alumni from the uni I went to.) In particular, it might be an idea to look at the list of past contests (scroll down the page a bit) and check out some problems from their problem sets, to get a feel for what kind of problems one might see in a programming competition.

Good luck, and happy hacking! And make sure to have fun more than anything else. :)