For your user case I’d suggest going s/h could be a good option, especially if you can find one like we did from a fellow GZ member, which was in perfect condition. Keeps the price down so less justification not to go for it! Also one less new device that needs to be made…
Like others, I’ve already made the argument above for going for the OLED over the original version - noting you’ll be using it sometimes handheld I’d definitely recommend the former, as the LCD is really dull (both in brightness and colours) in comparison.
I’m not a gamer so rely on my kids’ feedback - while they have access to a huge number of games on various platforms, their all-time favourites remain the two Switch Zeldas and (in one kid’s case) Animal Crossing; they’d argue the Switch is worth it just for Zelda!