there are two types of skill sets you need to develop in terms of becoming a better overall player:
Your base skill, the fundamentals, baiting, learning to deal with other chars/matchups, basically all the general non char specific information surrounding melee
then there is the char specific skill, this is knowledge of whatever char your playing, being able to choose the right moves in X scenerio, knowing how to di, what combo's you have on all the cast, best way to recover/edge guard, etc.
in my opinion, unless you're the type of person who develops char specific skill rapidly (i am not, when i pick up a new char i am in a state of confusion 'what move should i use here, or there, how should i approach/defend' i basiscally get overwhelmed with all these new options and forget to choose the best one and my focus lies on other things rather than my base skills, which would be baiting and other things), so unless ur the type of person who that comes second nature too, i think 1 char is best until you have a very strong base skill foundation
you can always watch video's and help develop char specific skill, it's a lot harder to develop yoru base skill unless you're 100% consistent with ur char specific skill though
if you can't do everything you want with your char 100% of the time then it's going to be harder to develop ur base skill
that's my view on it any way