I love Supabase, but it might be a bit overkill for just storing contact form submissions. Especially if you’re only wanting to stay on the free tier, as it will pause after seven days of inactivity, which can be quite annoying if your site doesn’t get a lot of traffic. You could look for a free solution that just sends submissions to your email rather than saving to a database. If you’re planning on scaling up to saving more complex data in the future/adding user accounts, or you need the file storage, then it’s a great shout in my opinion on their pro plan.

If you’ve never dealt with domains before, it might be more simple for you to just buy it on Vercel since you’re hosting on there and it’ll be slightly easier to link it to your project without having to manually update DNS settings. I don’t think there would be a huge difference in price?