This is mostly a security question, however, traditionally the "Remember Me" checkbox places a session cookie in the user's browser so as to "automatically" log the user in. Making the checkbox "remember" the user's username/password is a feature best left to the browser and could be unintuitive for users accustomed to the normal behavior.

I would go with the normal route of creating a session cookie - like you said, you can have this cookie expire to increase the security of the method. There is likely a very standard way of doing this depending on the technologies you are using to host/run your website.

This is mostly a security question, however, traditionally the "Remember Me" checkbox places a session cookie in the user's browser so as to "automatically" log the user in. Making the checkbox "remember" the user's username/password is a feature best left to the browser and could be unintuitive for users accustomed to the normal behavior.

I would go with the normal route of creating a session cookie - like you said, you can have this cookie expire to increase the security of the method. There is likely a very standard way of doing this depending on the technologies you are using to host/run your website.

Edit: Sullivan also has the good suggestion of naming this feature more properly (i.e., "Stay signed in").