The right Raspberry Pi for gaming will depend on what you want and need. Chances are you’ll need a model with an HDMI port, meaning you should not get a Raspberry Pi Pico as it lacks HDMI ports. You also need enough USB ports for controllers — at least two. The model also needs to support an SD or microSD card where your emulator and games will be stored.
Overall, either the Raspberry Pi 3B+ or the Pi 4 will fit your gaming needs. The are some differences between the two, and they fit different needs. For instance, the Pi 4 is a huge upgrade and comes with more RAM options that can support more complex games like those of the Nintendo 64. Once you find your Raspberry Pi, check out this guide on how to turn it into your very own gaming console.