PostgreSQL is a powerful and reliable object-relational database system. It's a great alternative for MySQL. It is as easy to set up, performs better and offers far more features.
To install PostgreSQL server run:
sudo aptitude install postgresql
Database users can be created in command line with createuser tool. Running the following command will create user 'kuba' who is not a superuser, can create databases, cannot create new roles and his password is stored encrypted. You will be asked to give new user's password as '-P' option is passed.
sudo su postgres -c 'createuser -S -d -R -E -P kuba'
Note: Run createuser with --help switch to get an overview of available options.
There is a similar tool for database creation called createdb:
createdb mydatabase
Note: Read about MySQL in my another post: MySQL installation in Ubuntu 10.04.