What do you expect from those games? Do you want to play magic or are you going for a free for all commander experience?

I recommend Commander for playing in a group, since it has lots of fun gameplay, there are plenty of powerful budget lists and basically all the cards ever printed (with very few exceptions) are legal, so you can play what you have and never have to worry about rotation. I recommend looking up some budget lists to start out with, as they are generally significantly more powerful than preconstructed decks (some exceptions apply, but those precons are no longer cheap), while not being all that much more expensive.

Alternatively, as others have suggested, Pauper is a fun format to play that is basically guaranteed to stay fairly cheap, due to all the legal cards being printed at common at some point.

I recommend looking through (budget) decklists for either format with your friends and then agree on which one looks more fun for your group.

My and my friends always liked brewing our own decks so to encourage that and discourage net decking we’ve come up with our own casual budget format we call Bargain. The only special rules are your maindeck must be $30 or less on mtg goldfish and your leftover money plus an additional $5 can go toward a sideboard. We just check every couple of months whether a deck has gone way over budget and we haven’t had the need to ban or restrict any cards yet.

Pauper is the obvious answer. It’s unique in that every card in the format is Common rarity, so that mitigates price already. Check out MTGGoldfish’s Metagame page for Pauper, which lists competitively viable decks and their price. Not sure how up to date it is, but it’s a good starting point!

It’s not the absolute cheapest, but I recommend trying out commander if you have not already done so. The value of the preconstructed decks is very high as they come with a bunch of useful rares. Some of these decks are as low as $20 on Amazon. Additionally, almost every card ever made is allowed to be played, and nothing ever rotates out like in standard format. It’s a casual format so if you don’t have a lot to spend on perfecting a deck, many people have several tiers of decks for more fair matchups. If it’s just you and your friends, most of the preconstructed commander decks are well matched. Also there are 100 unique cards in each deck, so there is a ton of variety even in one deck and it will take many games before you even see all the cards you have.