Magic: The Gathering

For sure pauper. It's a format where only commons are legal. There is quite a lot of power contained there like Lotus Petal, Brainstorm, or Gurmag Angler, but you don't even have to play those necessarily to get a good deck going.

If the meta hasn't switched a lot by now, Mono Red should still be super good, pretty much one of if not the best deck, and it would run you like 60-70€ maybe. That's pretty cheap all things considered. But you can get something good going for a lot less. Especially when considering casual play.

Pauper is a cheap format by design, since it's only commons.

Commander is cheap if you buy precons. Very different style of play compared to other formats though. If you want to play with 4 people, it's a great format.

There are also the pioneer or standard precons that Wizards occasionally puts out. They aren't great for actually playing competively in those formats, since Wizards likes to leave out important cards, but they are fun if you are new.

Technically, the cheapest in-paper format is Pauper. That's all commons, so it's almost guaranteed to be cheapest. However, if you're just looking to play casually with friends, chances are Commander will work better for you.

Commander is designed for casual play and you can buy an official precon (pre-constructed deck) for about $45, less if you can find a cheap one online. That's about the same as most competitive Pauper decks, maybe a little more or less (though a few Pauper decks can get significantly more expensive, like if they're running Snuff Out). Pauper is designed for 1v1 while Commander is designed for 3-5 players (could be more but the games will take a while). So if you're playing with multiple friends Commander will probably work better.

If you have a local game store you're getting cards from they probably have a whole shelf of Commander precons somewhere you can look through.

Second the other comment by @jake_eric@lemmy.world . Commander is a good way to enter the paper format.

However, before jumping in I'd recommend playing through the (totally free) Arena tutorial to understand the base mechanics. And don't hesitate to ask questions or to read all the cards! Commander is an eternal format, so it has a huge history, I don't even trust an old player who claims they know it all.

So there's a lot to learn, definitely start with a precon and learn what works or doesn't work for you.