I wanna start speedrunning Super Mario Bros. but I don't know if there are any limits on which emu to use, any recommendations?

There are many different emulation options. One I highly recommend is Nestopia. Its an nes emulator and it is pretty good. http://nestopia.sourceforge.net/ I also recommed fceux, which is common in many nes speedruns. You can download it here if you want: http://www.fceux.com/web/download.html

Fceux also has TAS compatibilty, if you wanna do one. With that all out of the way, Good luck running Super Mario Bros!