One of the more confusing aspects to 3DS hacking has, actually, nothing to do with the hack itself; it has to do with which version of your favourite classic games to play. A lot of the first-party games made for NES and Game Boy were released on Virtual Console, along with a handful of Game Gear and Game Boy Advance ones. Especially if you jailbroke specifically to emulate old games, you might get a bit confused by all the options available to you.
Option 1, obviously, is simply ignoring the Virtual Console releases and emulating everything on a dedicated console emulator. Option 2 is downloading all the VC releases you want to play and not using the emulator for those games. Option 3 is using New Super Ultimate Injector to create VC titles that did not actually exist.
NES.
Best option: VirtuaNES
The NES has been picked apart at a bare-metal level and is pretty well-understood at this stage. To that end, it's one of those systems that can be emulated on basically any piece of consumer electronics. The reason I'm recommending VirtuaNES instead of Virtual Console is mostly related to sound; Nintendo's official emulator uses weird anti-aliasing to smooth the waveforms out and it... doesn't really work. VirtuaNES's audio emulation is much easier to listen to.
Super NES.
Best option: Snes9x
This is really the only option for Old 3DS players. But, really, considering there were only, like, what? 6? Super NES games released for New 3DS? Snes9x will certainly unlock the full catalogue of Super NES games for mobile play. Well, except for the Super FX ones. While games like Star Wing, Yoshi's Island and Doom will load in Snes9x for 3DS, they won't play at full speed. Oh well, that's what Mednafen is for.
Game Boy (classic / Color / Advance).
Best option: Virtual Console
The one place where Virtual Console excels is in the Game Boy line. The reason is that the available hypervisor is a little more complicated to use and the available emulators don't work consistently across all hardware and OS revisions. While quite a few of the most popular Game Boy and Color games were released on VC (including some surprises, like Shantae and Rayman), there were only a scattering of GBA games available. In this case, I would recommend using New Super Ultimate Injector to create a completely new VC title. For more information, the Hacks Wiki has a guide on how to make that work. Unfortunately, you will require a Windows PC for this method. You might be able to get it to work on Linux using a Windows compatibility layer, but don't hold your breath. Also, have Visual Boy Advance-M handy so that you can create icon and banner images for the games you want to play. To achieve an official-looking effect, use the game's title screen.
Functionally, there is absolutely no difference between Open AGB Firm and Virtual Console, as both of them run GBA ROMs by leveraging the 3DS's in-built AGB_FIRM firmware. In both cases, the 3DS will need to unload its own OS to run the alternative firmware, it's just that Virtual Console does it automatically from within the home menu environment.
Virtual Boy.
Best option: Red Viper
Since Nintendo is Morbiusing the Virtual Boy for some reason, let's address the very conspicuous fact of its exclusion from 3DS Virtual Console. You'd think it would have been there, people asked why it wasn't, and Nintendo just kept saying "we'll look into it". While I don't know much about the Virtual Boy hardware (I vaguely remember seeing it for sale at Sears, but mum wouldn't let me near it for some reason), people have said that Red Viper does a better job at the faux-3D effect than the original hardware did. I won't speak to that, but the 3D illusion from Virtual Boy Wario Land lasts a lot longer than most 3DS games' does. Anyway, TL;DR, don't play Nintendo's stupid little game; wait for the inevitable ROM dumps of the unreleased and "new and improved" versions of those old, piece-of-crap games and just play them on Red Viper.
"Oh, but Nintendo says it'll make it possible in a future update to play VB games in colours other than red and black!" Big fat hairy deal. Red Viper already lets you do that.
Master System / Mega Drive / 32X / MegaCD.
Best option: Picodrive
It's convenient that all the 8- and 16-bit Sega systems can usually be emulated by a single program. In this case, it's Picodrive. The 32X and MegaCD stuff will not run at full-speed on Old 3DS, but what was there for those anyway? Doom? Sonic CD? Knuckes Chaotix? The only outlier here is Game Gear, which, for some unknown reason, Picodrive can't emulate. Well, or the SG-1000, I guess, but what was ever released on that except cracky ports of arcade games?
Game Gear.
Best option: Virtual Console
A scattering of Sega-published games for Game Gear were released on 3DS VC, otherwise you can use NSUI to create VC injects of whatever games you feel they missed.
NEC TurboGrafx-16.
Best option: TemperPCE
I'll admit, I don't know much about the TG-16. My only experience with it was with an old Win32 emulator called pcejin around about 2014, on which I played chiefly Batman and Neutopia. Honestly, I didn't know 3DS VC even had this system in it. According to the Wikipedia search I did as I was composing this document, there were only 4 TG-16 games ever released, and only in Japan (therefore, PC Engine, rather than TG-16); however, the precedent having been set, NSUI has the ability to create TG-16 injects. Given how little I know about the system, I'm just going to go ahead and recommend the emulator, simply because it can be run on top of the 3DS OS and you can change games without needing to unload anything.
Anything else.
Best option: Retroarch
There are a lot of systems that are either too specialised or too obscure for full-on dedicated emulators for 3DS. If you absolutely must play Congo Bongo on Sega SG-1000 or Dark Chambers for Atari 7800 on your New 2DS XL, Retroarch will make it possible. The thing that Universal-db calls "Retroarch" is actually lacking in any emulation cores, so it would save time to simply download the repository directly from Libretro. It's a bit more involved than simply downloading a program and then starting it up, in that it comes with a lot of junk cores that either do not work reliably, do not work at all, or are duplicated by more stable standalone emulators. For full prep and install instructions, see the Hacks Wiki tutorial.