C isn't outdated, C is awesome (but imperfect). C++ on the other hand is full of tacked on, largely unnecessary extensions that make the language enormously bloated. The best way to develop in C++, in my opinion, is to focus on C fundamentals and only sparingly use C++ features when they are absolutely necessary.
I should point out here that I hold the unpopular opinion that Object Oriented Programming and almost everything that grew from it is not only useless, but actually harmful. Much of C++ is designed to support that programming paradigm. So if you like OOP, well, you'll need to use C++ features.
C programs are mostly compatible with C++, but there is some divergence post-C89. It's kind of like the difference between Python 2 and Python 3, minor syntax differences and a few specific rule changes. You probably will not have issues with this starting out. When I was learning C I accidentally compiled all my programs as C++ for weeks and I never once had a program fail to compile because something I'd written didn't work in C++.
I recommend at least running through Casey Muratori's Handmade Hero Intro to C videos:
https://www.youtube.com/watch?v=F3ntGDm6...MLNDd3ASRp
You can get K&R --
The C Programming Language 2nd Ed, by Kernighan and Ritchie, the guys who wrote the C language -- here, it's worth reading through and keeping on hand:
http://yunus.hacettepe.edu.tr/~yurdugul/3/C/c.pdf (PDF)
I use tutorialspoint.com a lot as a reference for the C standard library when I'm programming as well.
https://www.tutorialspoint.com/c_standard_library/
I have a bunch of other resources for C, I'll put together a list at some point soon. Sorry, but I don't have C++ specific resources to recommend. Cuz C++ is shit.
Really it's because I simply never use more than a couple C++ features in my code, and I don't use C++ libraries at all. I use a handful of C libraries from trusted developers for things I'm not very good at yet (graphics, for example) and otherwise write my own libraries.
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I highly recommend Brian Will's videos on youtube, too, just in general:
https://www.youtube.com/user/briantwill/playlists
Lots of short and sweet content there.