C# - Best Way To Deal With DB Connection In The DAL - Create Or Pass?

I want my Data Access Layer to be built very modular.Therefore I have data retrieval methods that sometimes are called directly from the business layer and sometimes are called by other data retrieval methods to create object dependencies.What is the best way to deal with database connections in the DAL?

a) Create a new connection in every method and dispose it afterwards.Good: Easy to write and to work with.
Bad: Many connections are being opened and closed. (performance?)

b) Pass the connection as an (optional) argument.Good: I could reuse an open connection for multiple commands.Bad: I have to keep track of the ownership of the connection (who has to close it?) and cannot use the very neat "using" statements.c) Something else? (Connection as singleton maybe?)This is the first time I am writing a real DAL so I really could use some help from you experienced folks.EDIT: As it seems to matter, it's an ASP.Net Website Project.