Fully upgraded set of Climbing gear, period. I have almost every piece of clothing you could want, and have fully upgraded it all too. The only stuff I refuse to get are all the jewelry items.
So, when required by the elements, water, etc. I change into the appropriate gear (snowquill, gerudo, flamebreaker, zora, etc.). I use stealth/sheikah gear only if I REALLY need it. Barbarian gear when fighting tough enemies. I also, of course, use the snow/sand boots as req'd in those environments. And, I have the monster masks to use when I feel like screwing w/ the enemies, or more easily getting past them without going way around them.
Honestly, after that, I feel that every other piece of clothing (or armor, if you insist on calling a shirt "armor") is completely unnecessary, and only there for "looks". Nothing wrong with that, but I'm not wasting any time changing clothing all the time just because of how it looks. To me, all "outfits" are purely functional, and the set bonuses you get with them is what I'm after.
Hell, if the climbing gear make you look like a drunk clown, I'd still wear it all the time because it's THE most functional set of clothing if you like running around all over the map going anywhere you wanna go.