Can I choose the order in which these effects trigger in Yu-Gi-Oh?
In which order do I execute them? Can I choose?


Yes, you can choose.

Both effects are mandatory, so you have to activate them eventually. 

As they both happen at the same time, and because it's your turn you chose which effect goes first, and each one goes in a separate chain (naturally you'll want Inaba to go first).

For reference, lets consider this wiki page, with my emphasis:


  ... effects that activate "During the […] Phase…" or "At the end of the […] Phase…", such as "Gladiator Beast" monsters. Instead, each effect activates as Chain Link 1 of its own Chain.


Furthermore, on that same page they indicate the following (which is based from the Official Rulebook p. 50, 3rd part):


  If multiple effects fall into the same category [mandatory/optional], the player that activates them chooses the order in which they are activated