I'm not sure about the database part, but for static hosting we use NearlyFreeSpeech.net (https://www.nearlyfreespeech.net/ https://www.nearlyfreespeech.net/),

I'm not sure about the database part, but for static hosting we use NearlyFreeSpeech.net (https://www.nearlyfreespeech.net/ https://www.nearlyfreespeech.net/), its a pay as you go service. Pretty perfect for when you don't know for sure what you'll need. You might want to check them out and read about what else they offer to see if it fits your need. I've been really happy so far.