Richard MacCutchan wrote in his comment to the question:
You need good programming experience to create something as complex as a billing project.
And this is the key.
If you had this experience, you would probably immediately realize that the choice of the database is just one of the many aspects you need to decide on, and that the choice is not that simple, it should be based on the detail of your project, from its goals to some requirements detail. However, I don't want to discourage you, as it's impossible to gain experience without making decision and doing the job.
I would not recommend
Access, because it is proprietary and not even client-server (is a file-server based tool). To properly choose the database server, you may need to try out some and perhaps prototype a small part of development with those you want to consider. Please see:
http://en.wikipedia.org/wiki/List_of_relational_database_management_systems,
http://en.wikipedia.org/wiki/Comparison_of_relational_database_management_systems.
See also
http://en.wikipedia.org/wiki/Comparison_of_object-relational_database_management_systems.
Congratulations with April 1st! :-)
I would like to use the occasion to invite everyone to see my new 1 of April publication and have some fun:
Some Programming Approaches to "Neuro-Linguistic Programming".
Participation in this game in Comments and Discussions is especially encouraged.
Thank you.
—SA