Another notation convention is that, to be strictly correct, if the time signature is in quarters, a quarter note should only fall on the beat. Thus, a measure of 4/4 time which started with an eighth then a quarter would be technically incorrect, since the quarter would fall on the half beat. The correct notation in this case would be an eighth note followed by tied eighth notes.

That said, I think it's honored more in the breach and I certainly am not uncomfortable reading music with quarters/halves whathaveyou starting on the half beat.