Justin DeLay, Director of Product and Category Marketing at Reverb, drives home just how important the computer is: "You can strip away everything else and as long as you have a computer you can still create music," he told me. He suggests you "spend the money on a good computer and get other gear -- such as audio interfaces, mics, headphones, etc. -- used or at reasonable price points."
But, truthfully, you can do quite a lot with whatever computer you have on hand. Joe Pecora, the engineer and producer at Red Room Studio, says your set up "could be as simple as an iPhone/iPad with Garage band." (I know someone who recorded an entire album this way.) While he agrees that the most important part is your computer, he argues it doesn't have to be super powerful. It doesn't even have to be a desktop. JDilla famously created many of his beats on a Roland SP303, and you can basically recreate that experience with an iPad and the $4 Koala Sampler for iOS. And don't forget that Gorillaz recorded an entire album on an iPad.
Which leads us to the next thing you'll need: a DAW, or digital audio workstation. If you're a Mac user, then you're lucky enough to have access to Garage Band, a surprisingly capable free option. And upgrading to Logic Pro X, the same DAW used to record When We All Fall Asleep, Where Do We Go?, is only a $200 investment. If you're on Windows (or just don't like Logic), I often recommend Ableton Live (starting at $99). But honestly there are plenty of great options out there, like FL Studio, BitWig and Cubase all of which start at $99. And often, stripped down versions come free as part of a software bundle when you buy music-making hardware like MIDI controllers and audio interfaces.
Speaking of which, one of the first additions to your studio should be a MIDI controller. DeLay says this is a piece of gear often overlooked by beginners. "It's not just for playing keyboard sounds," he explained, "it can be used to write drums and percussion, to control mixes and more. It's the creative interface of music production, and you don't have to play the piano in order to harness its power."