Fruit – How to choose to avoid brown stringy fibres in avocado

Depends on if you'll buy for instant consumption or for storage.

If you want to eat/prepare them right away, you want an avocado that feels soft on the inside, when pressing them they will cede and have that soft feeling ripe avocado has. It shouldn't cede very much though, as those are past their prime. The very good ones even smell in a nice avocadoey way a bit (or maybe that's just my insanity.)

If you want to prepare them later, you want firm ones that cede only a tiny little bit (the rock hard ones mostly never ripen in my experience,) you then store them in a porous bag (the typical brown paper bag or a newspaper) to let them ripe. To speed up the ripening, you can add an apple to the bag.

See also this related question

You're correct - it's a myth, as is adding something acidic to it like lemon juice--see explanation here. As you said, what causes it to brown is the oxidation, and that's just exposure to the air. If you wrap a cut avocado (or guacamole) in plastic wrap so there's no air space between the wrap and the avocado, then it will stay green longer than areas where air is getting to it.