Does independent colony somewhere in the depths of New Eden count? No, okay. Well, ICily my main moved from Saisio, to Jita, to an independent colony detatched from the Empire's control but she was a capsuleer.
Before answering, I need to define a set of considerations:
Given that some aspects of each Empire had never been delved into, thus making a choice like that somewhat limited.
Given that the same Empire can have gradations of itself: I would expect Caldari in Jita to be much more cosmopolitan and open than Caldari in Corporate colonies far away from the main trade routes. Similarly I would expect there would be more "down to earth" gallente the further you move away from Caille and its entertainment districts. Just like in the real world where the culture of international capitals is not the same as the one of rural areas even while being the same country.
Given that there are other factions, such as Pirates and SoE, which you didn't include but which do have a foothold in New Eden and which have different ways of doing things than the Empires.
I think it would be either Caldari or Gallente. I'm not religious in the slightest so Amarr wouldn't really be my thing, I believe in the freedom to pursue innovation and careers, for sure not in an holy, all seeing god. On the Minmatar tribality, I understand it but at the same time... at the core, I'm an independent operator.
I would be Caldari for the structure, there are rules and rules are followed. True that the Caldari structure can be stiffling but then, if you find the right spot in the corporate ladder, I think it's not as bad as the Gallente propaganda make it look like. And if you're shrewd enough... bringing results pays and you can climb the corporate ladder.
I would be Gallente for the freedom to pursue things, both from a career point of view and from a personal view. Gallente can be a very innovative Empire because they are not as restricted by rules and dogmas as Caldari and Amarr ones. However, they do pay on missing a tight focus, which for example the Caldari, with their preservation of the State, have. On the opposite, I wouldn't be that much interested in entertainment and debauchery in themselves, they don't sell that well with me.
In truth, I would probably sit somewhere in the middle between the two. Either a Gallente with an appreciation for certain Caldari facets or a Caldari with an appreciation for certain Gallent facets. Not a good place to be in a polarizing world, isn't it?