I have been gifted a 360. Which game should I play first

This choice seems very dependent on what you actually like in games and what you've already played.

Minecraft is objectively the best game of the bunch, at least if you're the type that likes Minecraft, but you also almost certainly can play a better version of Minecraft on some other system. It runs on everything from your smart phone to your toaster and there's nothing wrong with the 360 version when taken on its own but it's inferior to anything that's up to date with the latest patches and improvements.

Banjo Kazooie Nuts and Bolts is a divisive game. If you're looking for a 3-D platformer and are a fan of the prior games you'll likely hate it. However some people really enjoy its weird vehicle building gameplay and the dumb stuff you can do. It's a game you may really enjoy or may hate. It should be noted that its 360 performance is pretty bad and it plays and looks better on Xbox One X or Xbox Series consoles so if you're considering getting one of those some day you may want to wait.

Viva Pinata Trouble in Paradise (my vote) is a very good game, provided again that you like its style of gameplay. If you're an action gamer you'll probably like the other two more, but if you can vibe with more of a sims/builder experience then this is probably your best bet. Unlike Minecraft it's not available everywhere else (though it is on Xbox One and Series) and unlike Banjo Kazooie Nuts and Bolts it wasn't really divisive (though it's not for everyone.) The one exception would be if you already played Viva Pinata because it's arguably more of an expansion pack than a true sequel, but it has a great aesthetic, good gameplay, and relatively broad appeal.

Nuts N Bolts is a dark horse masterpiece

I want to make it clear I will be playing all of these. I've played Minecraft plenty of times in the past, it's a comfort game. But I think I'm gonna choose one of the other two. I'm still waiting for all of them to download though, so I'll look back at this in the morning

IF you want to start playing now, just get Geometry Wars. ^_^

Asura's Wrath