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.