- https://retropie.org.uk/
Anyone in the market for hardware, I've found that the abilities of various devices tend to be overstated. Pi2 was in fact good enough for close-to-perfect NES, almost good enough for perfect SNES (fine for many games if you can tolerate the occasional slowdown or audio glitches), could play Mario64 acceptably but pretty much no other N64 games. Bizarrely decent at Playstation.
I'd imagine the Pi3 is pulls off SNES very well, just judging from the specs, though I don't have one yet. Be aware that these games will not look right without beefier hardware that can handle CRT shaders to (sort-of) correctly fuzzy-up the image. So, not a Pi. I now run Lakka on an Asus chromebox, which was about double the price of a Pi with a decent power adapter and not-hideous case, but can do the CRT shader thing and handles later consoles much, much better. Emulation on x86 tends to be more stable and better supported (faster) in general, so know you'll be on second-class (though rapidly improving!) platform if you go ARM.
Try out several controllers before settling. I found that the easiest solution (XBox360) failed my usual test of Punch Out and Super Mario. Couldn't block or dodge worth a damn in Punch Out (unsurprising given the 360's Dpad's reputation) and kept running into bottomless pits in Mario (I found switching between the "A" and "B" face buttons to be too slow). The 360 controller made it feel like the emulator input was lagging, but it in fact wasn't. PS3 controller works well for me. Wii Classic Controller Pro is even better, but I have yet to find a to-USB adapter that isn't messed up in one way or another—last one I tried would periodically register a bunch of wild analog stick input for no obvious reason, making it useless for N64 and Playstation. A big Retroarch-specific benefit of a PS3 or Wii Classic Controller is that you can use their home/menu buttons to bounce to the Retroarch menu, saving you from configuring a button combo for that—IIRC the 360 controller wouldn't let me use its home button for that purpose.
That's a problem with the emulator, not the hardware. I have a work-in-progress Mupen64Plus fork that can play all N64 games at full speed or better on the Pi 2 with only minor occasional slowdowns (that should all be fixable). The problem is that the emulator plugins were all designed for GL 1.x era fixed function hardware, which is very different from what you need to make software run well on tiled architectures like the VideoCore IV. It's not easy to get them running—I had to add an SSA-based optimizing shader compiler, for example—but it all ends up working out fine in the end.
I would like to try running N64 games on even cheaper hardware like the C.H.I.P. at some point. I think they have a good chance at running at full speed.
The biggest problem with the Raspberry Pi for this kind of stuff is that the software, which mostly consists of lightly optimized ports of old emulators written for Windows, holds the hardware back. If you compare instructions-per-clock of CPUs and fill rates of console GPUs from that era with the relevant hardware on even cheap modern mobile SoCs, the latter blow the former away. It's just that the games of that era pushed the hardware to its limits, while the emulators on the Pi don't even come close.
A little pedantic, but Lakka is based on OpenELEC (and may have switched to LibreELEC by now). OpenELEC/LibreELEC are buildroot based OSs that boot straight into Kodi. Neither are affiliated with the Kodi project - but the devs get along and communicate.
Getting wireless set up on it is a PITA, unfortunately. You can plug in a USB stick full of games but you won't have access to its online cores (=system emulators) updating functionality. I'd recommend Ethernet if you can manage it.
The best parts are the above-average, very responsive menu and that all the cores speak to a unified I/O API (libretro) which smooths out most of the usual problems with multi-emulator systems.
Last time I tried this, some of my favorite games were super laggy (Yoshi's Island, Super Mario RPG) presumably due to having to emulate additional processors (Super FX, SA-1, etc.)
edit: Oh wait, this is NES we are talking about. Nevermind, I'm sure NES runs fine. I'll leave my comment up for anyone wanting to talk about SNES emulation.
Retropie is amazing, but there are a lot of emulator options available, and some don't seem to work out of the box.
 I guess it depends on how sensitive you are to lag in the first place...
But this is official, with licenced legit games from Nintendo, so some people prefer that.