An other option is to buy an Amazon Fire TV (stick) or Nvidia Shield (TV). In that case you can also play the Taxman remasters of Sonic 1, 2 and CD on your TV (which is also possible with OUYA). And if you use MD.emu Sonic 3 & Knuckles should be no problem.
These days I normally go with the Xbox arcade versions of Sonic 3 and S&K which has Sonic 3 & Knuckles as "Extra Content". Its in HD and is now backwards compatible on Xbox One. I'm sure this is the same on PS3 too. I also have it unlocked on Sonic Mega Collection but to unlock it you have to load up a few of the other games multiple times to get it to unlock. Mega collection is however pretty cheap these days and available on PS2 , Xbox and GameCube.
Truth be told, if it weren't for me always having my Genesis hooked up all the time, my system of choice for playing S3&K would probably be my WiiU of all things. For one, it gives me the option of playing either legit or not-so-legit copies thanks to homebrew. Second, (provided I don't use Wii mode) the signal sent to my TV is 1080p over HDMI (as opposed to my Genesis for which I only have composite cables.)
Not a proper Wii U release. You can either Homebrew it to play Emulators, or use the Wii channel on there to play the Virtual Console release. I don't know how safe the Wii U is to softmod just yet but since Nintendo have dropped it for the Switch, the temptation is starting to get to me.
How many people here actually prefer to play S3K with a scaling filter? I must not be the only one, right? RIGHT???
Please note that if you live in a PAL country, the Virtual Console version will play in 50Hz mode, which I've read that the Wii U doesn't support well and just doubles each 5th frame, not registering button inputs on the "fake" 6th frame.
I modded my Wii U virtual Wii pretty easily. I've also done it twice on real Wiis. Still haven't messed anything up.
Sonic 3 Complete on MD.emu for Android. It is the best emu since the real thing. I can attest to it as it is the only one I've used since 2011 and no other is as user-friendly, reliable and professional. It is part of Robert Broglia's line of Android emulators for about a dozen classic consoles. Sonic 3 Complete speaks for itself so no explanation needed there.
Good point on this. My above advice should be for US Virtual Console only. As a UK boi myself, It's always been a minefield not knowing if you'll be getting a 50hz or 60hz game with what you pay for. PS3's PSN was a bit of a pain for that as well. My happy face when I bought the PSN release of Capcom vs SNK, only for it to become a sad face as I realised it was the PAL PS2 50hz only release. The slowdown was real that day... I sometimes like messing around with Retroarch shaders for CRT effects, scanlines, etc. Depending on the game I'll also use Bilinear filtering, but this is on a game-by-game basis. Something like Sonic I'll play with clean sharp pixels (green hill waterfall posters need not respond :^) ) , but something like Donkey Kong Country I'll filter it a little as I always feel the game natively benefits from a little anti-aliasing effect.