My recommendation to you is to take full advantage of the eShop. There are so many great titles there to choose from, and most for under $20, which seems to be right in your budget. I also recommend picking up a micro SD card soon, preferably when they're on sale. the 64 GB are adequate, but the 128 GB gives you plenty of breathing room for plenty of years. I'm sure you might be one of those physical only gamers, but the ability to switch from game to game on the fly is one of the greatest benefits of the Switch and being able to skip the step of finding the game card and putting it in the system is super nice.
A few games: Snipperclips is a great couch co-op title. And Breath of the Wild, while ginormous, can be played in small doses here and there. The open ended nature of the game means you don't really have to continue on one certain path and remmeber where you are at, etc. Hollow Knight is an absolutely great indie title that is well beyond what should be expected from any 2D game.
Definitely get a carrying case for your Switch. The last thing you want to do is drop that thing and really have a problem. Also, a charging solution for your joycons and/or pro controller (which is a great purchase) will also come in handy.
But mostly, I hope you enjoy the system. Sorry you had joycon issues. We've all been there, unfortuantely. It sucks that even in the newsest model you had this problem.