The best way to get something that will work for you is to design it and build it yourself.
I would recommend not using Microsoft Access. Microsoft Access makes an OK single user database, but it more than one person will be accessing it at a time performance will begin to degrade. I would recommend looking at either MySQL or Microsoft SQL Server Express. Personally I would use Microsoft SQL Server Express.
SQL Server Express is a free version of Microsoft’s SQL Server database product. It contains most of the features and it’s only limit is that it only uses a single processor, 1 Gig of RAM and databases of up to 4 GB in size which should be plenty for your uses.
Most hosting providers will offer a service which gives you access to either a Microsoft SQL Server or MySQL database. If Microsoft SQL Server is offered it will be the full SQL Server edition not the free Express edition so it will be very powerful.
If you don’t have anyone on staff who can design this database for you it should only take a database professional a few hours to design the database for you.