Ignoring the part of your question about marketable skills, my opinion is that C is an excellent first language. Most of the lesson plans for languages higher than C want you to learn object oriented design pretty quickly. For myself, wanting to learn how to program without first learning OOD was the reason I decided to learn C. I believe I will probably be able to know everything in the language reasonably well after 6 months, but everyone can choose how long they want to do it. I had decided to purchase a textbook and do every exercise in the book which concerns C, and that is what will take me six months. I am about five months in, and I'll finish next month. This is the book that I chose for this task. Admittedly, only 14 chapters of this book are about C while the rest is C++, and occasionally the exercises the authors write up don't make sense. I did, however, try to learn a few different ways, and this I feel is the best way for me.
So, again, the fact that C is not made for object oriented design makes it a language which is easier to learn than most other languages.