Hi Pablo,
Hope you are doing well. As per the description given above, if we understand correctly, then you are willing to make drawing tool as default selection to add comments on a PDF file, every time you open Acrobat DC. Is that right?
There's no such settings within Acrobat's preferences that can be enabled to make tool selection by default. You can make Hand tool to act as an Select tool, by changing preferences under Acrobat>Edit>General.
What best we can suggest here is to use the Keyboard shortcut for quick selection of Sticky Notes to add comment on PDF. Here is a list of all the Keystroke that can make your job a bit easy https://helpx.adobe.com/acrobat/using/keyboard-shortcuts.html
Thanks,
Akanchha