Re: Hey look, a poll.
Parody characters have the advantage that you can pull from the existing lore and story so that you can go right into your dirty perverted fan fiction without having to set up too much background and lore, since that has already been done. It is easy to take a story and say, "Up to this point everything was normal, but then blah blah blah secret love blah blah blah learned seduction skills blah blah blah magical giant internet penis."
Popular characters also have the benefit of being popular. It is really fun to see them getting the sweet reward of sexual release, or infamous characters suffer the humiliation of sexual torment if you're into that, as it tickles that part of the hind-brain that wondering if this or that person is getting their doctor recommended horizontal bogey time.
The downside is that you can easily get the characterisation wrong, turning your parody into a mockery of the original, or a cheap doppelganger with the same name and face as the original.
Original characters are a lot less stressful to write, as you only have to keep track of what you come up with. This makes them more intuitive for you, the creator, to work with.
The downside is that you have to put more effort into creating them, and more effort into establishing the character to the audience. Watching random people bone get's boring fast. It's the emotions behind the happy fun tiem that really engages an audience and will give you return viewers/readers/players.
So do whatever the fuck you want. Just put as much thought, effort and passion as you can afford to. Look up design principles and stuff to figure out how much work you should be doing. Especially if this is your first project.