This seems like an interesting game to speedrun and I am wondering how to begin. Currently I am just trying to finish the game casually and then I am going to try for a+ times, is this a good way to begin to speedrun this game.

Yes it is. You can just finish the game several times in any% too, and sometime, watch a speedrun or a live on twitch :)

"try for a+ times, is this a good way to begin to speedrun this game." Well it would be better if you learnt the way to complete levels, then practiced your levels. Also, as Gaurox said, watching runs while training is always a good idea.