I am currently running 1 droplet and within that it's running 1 web server and 1 database (MySQL).
My plan is to move out the database into a server of it's own.
The database is still fairly small, it's only at 250MB....
It depends on how much time/energy you want to dedicate to maintain/update/backup your DB server. If you'd rather focus on something else, you could spin up your own Droplet. However, if you trust DO to have better me...
DigitalOcean Managed MySQL Database