If you can only focus on one game, pick Breath of the Wild. If you have the time for both, I would only say to play Odyssey first because you will, most likely, put way less time into it. I think I logged 35 hours in Mario and 165+ in Breath of the Wild. I have gone back and played more BotW after beating it but not so with Mario. If you're a completionist though then you might feel compelled to put another 15 hours into Mario to get everything.
There have already been a lot of great suggestions for what to play, so I will just say to check out the Octopath Traveler demo! Also, Aegis Defenders is a fun little game if you're into the Adventure genre. It is a 2D platformer with mostly environmental puzzle solving and a tower defense segment at the end of each level. It has a few dialogue options that are there to encourage you to figure out the characters, and reward you for doing well, but don't really effect the story. The artist took some inspiration from Studio Ghibli for character design/style and there is definitely an "anime" feel to the plot.