You can buy FPGA consoles like the Mister that bring vintage consoles [up to PS1 or so] back with high accuracy and low-latency. The most accurate models are compatible with the classic peripherals.
They are trying to build an FPGA N64 right now, but it has run into delays. I think an FPGA N64 is particularly valuable right now, since that console can be hard to emulate. In the meantime, you could play the recompilations / decompilations, in which some of the most beloved N64 games are compiled to run natively on PC and other systems. This means you can play those games using any controls, and any screen, at 60 - 240 fps.