Well I know it's a bit on the extreme side of things, if you were willing to drop nearly $400 you could get the SuperNT HDMI console, and then the SD2SNES which basically runs once they patch in the SDD1 every single NTSC and PAL game on the market minus 2-3 Japanese obscure titles that'll never get added due to the size of them beyond the scope of the FPGA itself.
If you had those you could enjoy the entire SNES library using just the one kit cart with no worries at all and no emulation either. But if you're going budget, I'd get something like the Nvidia Shield console and load a SNES emulator to it, then get a USB SNES wired controller for the experience and be done with it that way just side loading all the ROMS you care about.
Cheapest logical choice, SNES CE + Hakchi mod hack so you can throw virtually any SNES game at it and they more or less all work since the emulator in the SNES CE covers the DSP, C4 (Megamanx2/3), SA1 (Mario RPG, Kirbys), and the FX games (Starfox, Yoshi, Doom, etc.) I'd guess like 98-99% compatibility going that route.