I have my own application. My client wants me to use their web service. This web service sends some data to my database. For this, my client wants a certificate from me. In this scenario, what kind of certificate should I provide?
If the client web services have access to the internet or they have a local CA, then I would suggest that you use CA signed certificates.
Otherwise it is fine to use self signed certificates in your case but it will be a headache especially if the client has multiple web services and you want to update the certificate.