It could go either way, really - when I first started out, I tended to go for the ~obvious ships like Pokéshipping, Contestshipping, etc, probably cause those were the ones that were mentioned most. Then I kind of outgrew those (i.e. discovered slash. XD though I still like Pokéshipping), but I still tended to like the main character pairings so I don't know if you'd call those obscure.
Now, a lot of my favourite ships are Pokémon/Pokémon that few people know of, so I'm obscure in that sense, I guess. In general I think I've gone from being an animé-focused shipper to a game-focused one, so I tend to ship the gym leaders/elite four and stuff more than I do the animé characters. Possibly because I've completely failed at keeping up with the animé. =P So yeah - I've been both but you'd probably classify me as an obscure shipper these days. (wow, that was needlessly long, sorry. ^^; )