For small projects I'd remove the bit about 'saving money' being a reason to use VPS. If you want to get better at Linux, then by all means. However, if you'd like to save money, assuming you place any value on your own time, it's just not worth it.

If your project fits in a "serverless" environment use Vercel or Netlify for free. If not, use the Fly free tier or pay a small amount of money per month. Use Supabase or Planescale for the db.

For the price of $0-5/mo* you can deploy whatever you like, without managing the infrastructure. Then you can focus on building whatever it is you wanted to deploy.

* The asterisk is of course that these services usually cost quite a bit more if your usage goes beyond the free tier, but you can always move to a VPS at that point.