Hi Triple,
You generally want members to see content that non-members cannot see. That's the logic behind the Login Welcome Page: After a member logs in, they get to see special content specifically for them (the Login Welcome Page), which would direct them to other content that they can see (content that non-members cannot see).
If the member-only content is on the home page, then you'll need to do some advanced scripting to check if the person viewing the home page is a logged-in member. That makes things a bit more complicated than simply creating a separate page (the Login Welcome Page) for members-only.
If you want your Login Welcome page to be the home page, you can configure a Special Redirection URL for the Login Welcome Page. This can be done in
WP-Admin -> s2Member -> General Options -> Login Welcome Page (you'll see the redirection box at the bottom). Simply add the full URL to your home page (i.e.
http://example.com/) to that box.
Now after a member logs in, they will be redirected to the home page.
If you'd like the home page to then display some member-only content, you'll need to use the s2Member scripting feature to check if the visitor is logged in. You can read all about that here:
WP-Admin -> s2Member -> API / Scripting -> Simple / Shortcode Conditionals.
Does that answer your question?