Leyla H. answered 18d
Professional Spanish Interpreter AND Flute Performer ... for 20+ yrs!
Actually, I think you have answered your own question, and quite well, I might add. You perfectly described the placement and purpose of each element of a time signature.
You were also correct when you stated that 4/4 is a common time signature, so much so it is referred to as "common time" and is sometimes represented by the letter C, located where the time signature would be.
You may also see a letter C with a line through it (similar to the symbol for "cent"), which means "cut time" and can also be represented by the time signature 2/2.
To avoid confusion, let's take a time signature with different numbers on top and bottom: 3/4. This time signature means that the quarter note (bottom number) gets the beat, and there will be 3 beats (top number) per measure.
I hope this helps.