My advice is just to play Classic/All-Star with Tap Jump off and don't give up if you get frustrated. When it comes to learning new controls, it just takes patience and perseverance. Switching to a new controller, switching your control settings, switching buttons... all it takes is time. I've switched controllers twice and messed with my settings numerous times to improve my control output, all with success!
As for Tap Jump itself, I personally would keep it off 99% of the time. If you're playing a character that relies on their up tilts (which is a lot of characters.
![Mario :4mario: :4mario:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
,
![Pikachu :4pikachu: :4pikachu:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
,
![Megaman :4megaman: :4megaman:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
,
![Ike :4myfriends: :4myfriends:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
are a few I can think off the top of my head), you'll want Tap Jump off, while if you're playing a character that doesn't rely on their up tilt too much, like
![Ganondorf :4ganondorf: :4ganondorf:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
, it could be beneficial to keep it on. Generally, though, every character has some use for their up tilt, and you definitely don't want that option to go away.