I suggest a SNES style controller. It will easily handle both NES and SNES games. Three button Genesis/Mega Drive games also work fine. Six button Genesis games are a bit awkward, though.

My personal favorites are the Retrolink Dual link Capcom SNES controllers, the buffalo SNES clones, and the PS4 Hori Fighting commanders. The Hori is especially nice because of the six button layout and quality d pad, but they are more expensive. Be wary of the buffalo controllers as they are very nice, but they have ghost input issues (all three buffalos I own have that problem).

I do not like the 8bitdo wireless options personally. I have found them to be quite overpriced for what they do. They also have a significant problem with signal interference in my abode, but I have something like two dozen wireless devices running in the same apartment with 4 radios running at legal maximum signal. Your experience may vary.

Controllers for larger hands include the Hori Pokken controller, which is excellent but bulky. The xbox one controller honestly works pretty well and has a good pad, but it's large. The PS4 controller is expensive, but might be a good wireless option for small hands (I like the ps4 controller, but my wife has spider fingers so she likes the xbox).

Do not by the super cheap multi controller packs from Amazon. You would be better off playing Ninja Gaiden with a keyboard than using those things.