To generate an SSL certificate signing request (CSR) with key you can do this:
openssl req -nodes -newkey rsa:2048 -keyout bla.key -out bla.csr
This syntax does not force you to supply a password, which is convenient.
If you generate a CSR for startcom, you don’t have to fill in any fields; only the public key from the CSR is used. For other vendors, the common name is important; the domain name must be entered there.