C is a great language for understanding the deep inner workings of a computer (some people I've worked with claim that it's "assembler with a nicer syntax", but I"m not quite sure I'd go that far)
For web work, PHP is the most similar in syntax to C, but I'm not sure that it's really a great starting point (it's really easy to learn, but the people who learn to program in PHP early on seem to be blissfully unaware of... well... the last 30+ years of programming theory)
I would suggest python as a good place to look for building web apps. It will also give you the advantage of a different perspective on how programming languages should work, look, and feel. Variety is pretty important, imo, for really understanding what programming languages are capable of, and people who say you should learn only their one favourite language are pretty short sighted.
For an easy resource for getting into some basic python (that will also give you a bunch of background in an easy-to-digest way) I suggest buying Z. A Shaw's "Learn Python The Hard Way" - http://learnpythonthehardway.org/
That's the opinion of one programmer, though, and I'll shut up now before everyone else jumps in and tells you that "C is the one true language" or that "C is an outdated dinosaur", or that "If you're not using Ruby, we won't talk to you", or whatever else really passionate people like to say.
Learn other languages. It'll help you to understand them all better.