[c] How do I properly compare strings in C?

Use strcmp.

This is in string.h library, and is very popular. strcmp return 0 if the strings are equal. See this for an better explanation of what strcmp returns.

Basically, you have to do:

while (strcmp(check,input) != 0)

or

while (!strcmp(check,input))

or

while (strcmp(check,input))

You can check this, a tutorial on strcmp.