Your best bet is to buy a 3DS, and a Switch if you can afford both. The 3DS library is gigantic, and there are many classic Nintendo games available for it. I own both systems and still play my 3DS. It’s one of the best systems every created, and it complements the Switch very well since it has a much larger library and I can stick it in my pocket and run out the door.
Amazon still has 3DS systems available, or just get a 2DS if you don’t care about 3D:
https://www.amazon.com/Nintendo-3DS...95862a5e93be3d2d5f1742394c05f2&language=en_US
I recommend the following games:
Mario Kart 7
Monster Hunter Stories
Super Mario 3D Land
Yoshi’s Woolly World
Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey
The Legend of Zelda Ocarina of Time 3D
Donkey Kong Country Returns 3D
The Legend of Zelda: A Link Between Worlds
And that list is just a start, there are ton of other great games for the 3DS. Most of the 3DS games are also less expensive than Switch games too. Plus you get actual buttons, and two screens on the 3DS which make playing the games way better than on a phone (though I do love my iPhone, it’s just not as good for gaming).