Access is as simple as a database gets. Then to make it an "online searchable/editable database" you would need to use a dynamic web language such as ASP, PHP (use with MySQL database), ColdFusion, or JSP to take the job of the front end display. Think of them as substitute pages of HTML (static content).
Other databases include MySQL as mentioned, SQL Server, DB2, and Oracle... though the latter two are more difficult for a beginner.
Post in the correct forum and people will start you off on PHP with MySQL since they're free. In my opinion, ColdFusion (with any ODBC database) is the easiest to learn but it's not cheap nor widely supported.
You will need to consider other things such as who/where to host this from. Are you planning on creating all this yourself ?