I'd say to go with OoT as far as learning to speedrun. I've played it the most, that's why I started speedrunning it.
Above all, though, pick a Zelda game you have played a decent amount and at least beat the game 100% or do a challenge run (like a 3 Heart Run) before attempting a speedrun. Plus, you have to like the game enough to want to play it many times, especially if you want to go for a world record time. It ultimately depends on how much patience you have and what your goals are.
Furthermore, you usually have to change your mindset when you speedrun. Specifically I'm talking about detaching yourself from the game world and its inhabitants. It is very common to use glitches when speedrunning, and these glitches can potentially skip large portions of the game (the Wrong Warp glitch in OoT is a perfect example; it can be used to go directly from the Deku Tree to the end of the game).
As for the type of speedrun to start with, I highly recommend trying a glitchless any% speedrun (ie. beat the game without using glitches). Then, if you wish, you can research, learn, and practice glitches or strategies ("strats") and routes for the particular game you speedrun.