Before we start; no, this isn't a tutorial on how to get Luigi, Peach, Yoshi, or Toadette, but it's still just as easy to have as much fun with only the first 3 levels and Toad Rally; so here's how to make the most of those of us too cheap to pay $10 for an app. Even if it is way bigger than Pokémon GO.
Sure, Mario is fun and all, but if you're really a cool person, you'll play as Toad. You can unlock Toad by linking your game to your Nintendo account. For those of us that tried to complete the first #Pokemon challenge in Sun and Moon (which we failed really badly) then linking our account will be no problem, and if you didn't participate in that challenge, don't worry, making an account is really easy!
Get All Of The Pink, Purple And Black Coins
First and foremost; be a cool guy, get all of these coins. Not only do they greatly increase your coin intake for that level, but you'll probably kill a ton of goombas and koopas while trying to get all five in one run, which will only help you in Toad Rally. It also gives you 2 Toad Rally tickets every time you complete one set, which means you can get a total of 18 tickets just by doing these 3 levels (and if you link your Nintendo account you can get even more thanks to the challenges).
Play Lots Of Toad Rally
This is probably the most awesome thing ever, and if you're really good at it (like I am... not) then it's also a really good way to level up your kingdom! In Toad Rally you only have a little bit of time to get as many coins as possible, and if you beat enough enemies in the main story, they're worth more coins in Toad Rally, which is absolutely awesome!