There's good news and there's bad news. The next game in the Half-Life canon won't require the $1,000 Valve Index hardware to play. That's a bullet dodged. However, it will require some sort of PC-based VR setup, and that's going to be costly for anyone who's hellbent on playing the new Half-Life but isn't a virtual reality early(ish) adopter.
Let's get the obvious stuff out of the way upfront: You'll need a PC that's beefy enough to run VR. The various headsets have their own compatibility tools (although apparently Facebook discontinued Oculus'), but Road to VR has a catchall list of specs.
If you don't yet have a PC, your path to Half-Life: Alyx is a lot more expensive. Here are a bunch of pre-built gaming PCs on Amazon. They should all be VR-capable, but do your due diligence and individually research whichever one you might buy. Or, go ahead and build your own. It's a fun life experience that you won't regret (unless you critically screw something up which probably won't happen), and you end up with a PC that you're more attached to. Use PCPartPicker if you have no idea where to start.
Okay, now it's time to talk turkey. Valve has stated that Half-Life: Alyx will be compatible with all PC-based VR. If it can run SteamVR, it can run Half-Life: Alyx. The headsets that are explicitly mentioned are: