you are right, I was expecting to have also OLEDB or ODBC listed but there is only SQL Server and SQL Server Compact. Anyway if you are doing serious development at minimum use SQL Express or SQL Compact, both free and probably way better than old MS Access.
With the latest version of SQL Compact (4), it runs also in IIS and with Partial Trust so you can use it without any issue with your Hosting Provider, in case you do not want to pay for SQL connectivity.
like you find here: Microsoft SQL Server Compact 4.0
Enabled to work in the medium or partial trust environments in the web
servers, and can be easily deployed along with the website to the
third party website hosting service providers.