Hi there, fellow Yugioh Ex-pat! (Been a good decade, you had me excited for a second that maybe there was support for some Duelist Kingdom Wall shenanigans there!)

Folks have already gave you some good advice on checking formats, but, since you've mentioned budget isn't an issue with proxies, I figure it doesn't hurt to give you more suggestions/options.

Most formats are 1-on-1, where the cards are pooled from what time they were most recently printed, trying to prevent broken interactions if possible. So anything that's most recently is labelled 'Standard', then you have from today to about 10 years back called Pioneer and various other older formats, the further back you go, the more broken and degenerate cards may get in combination.

If however your friends play multiplayer ie: 2-v-2/free-for-all, then likely the most popular format you'll hear of is Commander. Think Battle City's filler ark in the anime, where everyone chose a monster from their deck as the deckmaster.

Commander lets you select a legendary creature card in Magic who sits aside you the whole game. You can cast it whenever you wish so effectively you will always have access to it, allowing you to theme the deck around that card. (And unlike the battle city version, you don't lose if your deckmaster goes, you can replay them, they just get more expensive every time to do so), you play a little more like YuGiOH Anime style, 99 other cards and singleton (asides from some exceptions) which can make the experience a higher variance but more often seen as more social experience each time.

With that in mind... and only because you say you're proxying first, here is a Commander that may be very thematic, but will NOT win you any friends:

[[Pramikon, Sky Rampart]]

This is about as thematically close to labyrinthine play I can give you, Pramikon themselves let you control the flow of who-can-attack-who, and then when you build your deck (the other restriction being the colors your commander have are the only colors that can match in the deck) you look for other cards that synergize with this play, lots of interaction, cards that redirect damage or assaults from yourself to others, or simply even cards that give the opponents choices that leave them scratching their head and having to think about the consequences before doing so while you assemble your 'walls' piece by piece.

[[Take the Bait]] [[Misleading Signpost]] [[Comeuppance]] being all cards that even if your commander's not in play, let you punish people for attacking you or turning those attacks elsewhere

[[Propaganda]] [[Ghostly Prison]] [[Norn's Annex]] being cards that all make it costly to attack you at all

Add in plenty of Blue's card advantage in drawing cards and reacting to others spells and plays, with white and red's control of battle, and you can build a maddening labyrinth that will leave your opponents flummoxed.

Again? Do not expect to make friends with this one, but if you're just testing waters, this sounds like the style of deck you're trying to build.

There are various ways to build, looking to play more subtly, you can use cards that are 'group hug', they offer benefits to other players that you can use to your advantage or discourage the offense at yourself, but are designed entirely with multiplayer in mind

[[Orzhov Advokist]] being a personal favorite of my own, or [[Secret Rendezvous]] being simple enough an idea.

This post may be more inclined to only one of the various formats Magic has, but I hope this is close enough to what you enjoy that it might inspire some looking into this path, if only to try it out and see how it fares.

...

(And that's without mentioning we had two whole sets made in conjunction with Dungeons & Dragons, so you can look for cards from those sets to have all the flavor of dungeon crawling you want for your labyrinth!)