If you arrange a Windows web host account you can upload your Access database and use it as it is, with ASP pages to allow querying, record display and so on.
If you want the less expensive hosting option of Apache/Linux/Unix you obviously have to convert your database content to MySQL.
There are several good commercial conversion programs - this is one I've been quite impressed with:
There are also lots of articles discussing how to manually convert:
Two relatively simple methods that spring to mind are to export your table contents as CSV files and import them into MySQL. If you have an MS SQL Server available you can export to MS SQL and round trip into MySQL, but this is where we start to get complicated.
I'd say you have to weight the pros of cheaper web hosting against the cons of having to learn PHP to interact with a MySQL database, once you manage to get the table contents transposed from Access. Unless you invest in a commercial conversion you will also have to rewrite your queries and MySQL is a bit of a culture shock after you've been used to Access.
If you want some in-depth info, post again and I'll happily explain many of the ins and outs along with a few how-to scenarios.
The actual conversion though, is possibly the least of your worries. A dynamic PHP site using an unfamiliar database product is possibly more of a learning curve than an ASP dynamic site using your existing database.
There's no ideal answer I'm afraid.
Post again if you want more.