All good. Okay so perhaps consider something like Scolipede? Given that Razzy's aiming for the championship she'd probably want something that has a little bit of strategy behind it, and Scolipede can be useful offensively and also for support (kinda), especially with speed boost. Plus I'd imagine if she hates fairy types that much she'd probably want something on her team to wreck them whenever she came across them, and a poison type could certainly help with that.
Another idea would be Altaria. Its a pretty decent Pokemon and would help cover Ramses's fighting type weakness, plus as Razzy is travelling pretty often having something to fly on would be useful for covering ground quickly. You'd have part of its weakness covered by Plus I mean, Altaria doesn't look very threatening and might appeal to a rather kind hearted person.
Fighting types have always struck me as being rather competitive Pokemon, as do fire types, and fighting will help cover some of the previously mentioned Pokemon's weaknesses, so why not something like Blaziken or Emboar? They're both pretty cool, and fairly useful, and you could choose which one you wanted depending on whether you were after things that were fast, or more tanky. They also both get access to some of the elemental punches, which would be good for coverage.
Given that there's a bit of a psychic type weakness in the above, perhaps a Dark type would be useful. You said you were thinking about Umbreon, and while that's less offensively orientated it could make a good attention regardless. Plus its freaking Umbreon its adorable. Anyways maybe some of those, or Pokemon that play similar roles would be useful to you.