Well first I wanna say that yokai.com is a really cool site so thanks for sharing that!
As for what I relate to, I will actually go with the Tanuki.
"Tanuki have a jovial nature, and delight in playing tricks on humans."
Delight. That alone is enough to sell me on them: fun loving pranksters. I personally wouldn't go so far as to harm anyone in particular or cause serious injuries (at least not intentionally) and just get a kick out of it, similar to fairies in that sense.
Being shapeshifters, it's also implied that in addition to their appearance (human, object, etc.) they also change clothes which is awesome! Are you kidding? A wardrobe limited only by my imagination and magical power? That's just the best! I might go in the human village and make my living as a model for painters or something hehe...
"In the ancient religions of the Japanese isles, tanuki were considered gods and rulers over all things in nature. With the introduction of Buddhism, they gradually lost their status."
"While tanuki are not generally feared or considered malicious, they are not entirely harmless either. Like humans, each one is a unique individual."
Those two things also caught my eye too as that would be (as an individual) my 'weakness' as a tanuki: I'd actively play pranks on Buddhist temples in particular for that very reason.
With that being said, my runner up and a yokai, who I would like to befriend, is the Fudakaeshi
I love the idea of being a "fuda ripper" to allow other yokai to pass through normally "yokai forbidden areas". I would be the "weird" Tanuki who would seek to befriend them and aid them in this as it would benefit both our kind. The potential synergy between the two interests me: I, the Tanuki, would make the Fudakaeshi's deceptions alluring through my shapeshifting ability (As I can also turn into an object, pretend to be money for instance) and this would constitute as a prank done mostly for fun as, even the Buddhists I wouldn't want to harm outright as much as annoy... lol.
As for how I'd fit into Gensokyo as a tanuki, I'd would work with Mamizou when convenient but not be under her wing outright as I'd prefer to do things my way. Of course, she'd be one of the few I would never prank out of respect for my fellow species, in addition to acknowledging her power and not wanting to burn the bridge with her.
Yes, I would prank Myouren temple specifically as previously stated, but also probably do so with the other religious sects too, mostly for fun and to tease those 'holier than thou' types. Naturally Reimu in particular would wanna whack me with her gohei, mostly since I'd tease her specifically by pretending to be offerings in her donation box only to then disappear when she's sleeping, tricking her further that someone stole her 'only donations'. It might get predictable though so I'd have to constantly find new ways to annoy her for fun.
I'd often seek to work together with others, mainly the fairies due to the 'prankster' nature (maybe even shapeshift into one!). I think I would avoid being outright hunted by remaining on that borderline of 'not too dangerous but very annoying'
Finally I'd have a 'calling card' to my pranks, inspired by the Furutsubaki no rei, using it's flowers as a sarcastic gift to the sick who seek assistance through faith specifically.
Anyway got a bit long, I kinda wanted to give some specifics as to why I picked a tanuki beyond "they're cute". I went through most of the shape shifting yokai on the site and the Tanuki did indeed speak out to me the most.