Oh, if you're not caught up on the previous games, I do think you'll be losing out quite a bit playing Alyx first. Trying to avoid spoiling too much, Alyx's story connects back to them in a way that feels pretty huge if you've played them and a way that I think might feel a bit nonsensical and emotionally empty if you haven't. Then again, I seem to care more about story, world-building, etc. than most, so others might disagree.
When Alyx originally came out for the Index, I was in a similar position having played no Half Life games, so I decided to play them first to get up to speed. I don't regret setting aside all that time since they're all fantastic games in their own right and made the Alyx experience even better.
In case you want to follow along, I played just enough Half Life 1 to get a feel for it in light of its historical significance, but then I continued with the very good, more modern fan remake, Black Mesa. Then came Half Life 2 (non-VR), then Half Life 2 Episode 1, and Half Life 2 Episode 2. These last two are continuations of the main story, so don't skip them. I mention that because I remember thinking something else originally due to their names.
I actually haven't played the VR version of HL2 yet, but I would save that for a later replay. VR naturally makes things more intense, so Alyx slowed its pacing to compensate, and HL2 dialing it back up makes it a natural followup gameplay-wise.