You can click the "View Rules" button on the leaderboard to read what's allowed and what's not. If you're looking for tutorials, you can find some of those on the "Guides" tab to the left. Also, if you have Discord, I'd recommend joining the server and you can find that link on the left as well.

There are plenty of runners for this game (more than 1000 for the main category) and most of them don't interact with the "community" so don't feel any pressure to do that. But there is a fairly active Mario discord that is friendly and willing to answer questions from new runners. Just keep learning the levels until you can finish the game, and submit a time - even if it's slow. As @roopert83 stated - read the listed rules first. The summary of the rules is that there are a number of "whitelisted" legal emulators and consoles. Among them is the NES classic which you mentioned. Completely legal. Be sure to video capture your entire screen and game sound and you should be good.

Most of all - enjoy the journey. I know I speak for several runners when I say I miss learning the game.

Good luck.

If you'd like to go onto the route of emulation, I would recommend Nestopia for real runs and FCEUX for practice. FCEUX is mainly used for save stating, so you can attempts levels over and over again. Nestopia doesn't allow TAS' to be created/played on it, which is why a majority of people trust that platform. For run advice, this video is one of the most helpful tools I use for this game. If you ever struggle with a level, check his tutorial out. He'll almost always have advice for whatever is haunting you. Good luck in your runs! :)

NES Classic is a good way to start out, but be aware that it runs at a slower frame rate than a normal NTSC NES. If you plan to take this game really far, I wouldn't recommend it as you would have to upgrade in the future.

Darpey gave some great advice, submit a run even if it's slow; you've got to start somewhere. The tutorial videos by Kosmic and Darbian are nice as they cover multiple methods to attack sections. Check out the guides on here, especially the animated gifs guide (props to Darpey again). Lastly, don't be discouraged by dying in this game. Matter of fact, be prepared to die a lot lol.

Have fun with all of this especially with learning the tricks. Some of the tricks in this game require a lot of patience and hard work but they payoff is pretty substantial as far as time saves go not to mention they just look cool.