Series Representation: I think this is a big draw for most people, including me. Smash Bros. brings a plethora of various Nintendo characters together to fight- the chance to represent a series that fans love is part of the fun, I think. This is the option I voted on.
Character Representation: While I do like to see some character diversity in each Smash Bros. roster, I'm more for balancing the gender and human/non-human ratios, not so much the hero/heroine/villain ones. I don't mind having more antagonistic characters though, we probably could use a few more, but I'm personally more interested in seeing a balanced roster in terms of, well, gender and all that. But in all seriousness, this isn't a huge factor for me.
Fighting Style: I'm not a competitive player, but I imagine most people want each newcomer to have some viable tournament potential. I'm not terribly interested in playstyles that are necessarily new, but, when you think about it, more diverse playstyles lend to better representation of the characters and series. And different playstyles can be fun- I'm trying my hand with Villager and Robin a lot lately, and their strategies are somewhat different from a number of other fighters, but at some point I start to understand how to play as them, and it can feel pretty satisfying. I would say this is the second-biggest factor for me.
Bias: Personal bias for a character getting in just because you plain like them, I understand. I'm on that boat, though only with Banjo and Kazooie as possible newcomers, but I know that's pretty much not happening. (And at this rate, it's probably better that way.) But I don't have any interest in playing as a character I'm attracted to. I just don't. I don't see the draw. I know others do, and that's fine, but, bias in that way, I guess, is not for me. General and platonic bias for a character you like can be appealing for the Smash games though, it influences fan-favorites getting in. At least, I think it does, like Lucina and Mewtwo. Heck, it might apply for Dr. Mario.
Third Party Characters: I don't know what to think about this. I don't have a problem with characters like Sonic and Snake getting in and whatnot, but I think I personally draw a line where some third party characters, in my opinion, just shouldn't be in Smash. Maybe it's just me, but I think I feel that if certain characters, especially ones not related with Nintendo (take Goku, for example), became playable in Smash, then the series would feel more... cheap? Something like that. It just doesn't feel right to me. However, if they use third party characters like Mega Man and Sonic, which feel a lot more fitting, I'm okay with it. I don't really desire to see any more third party characters make it in at this point.
I apologize if this is a long post. Basically, I consider series representation to be the thing I want most in a newcomer, and fighting style is the thing I want second-most.