http://www.famitsu.com/news/201304/23032048.html
This article has more screens. Pretty much all the info in it has been covered before.
Yes those main menu screens have clear options on them.
The Training tab (mislabeled as VS tab in the screenshot) has Tutorial Mode, Training Mode and Challenge Mode as its selectable options.
The Story tab has Story Mode, "Teach Me More! Miss Litchi" and "Glossary" as its options.
You can probably already guess what the remaining 4 tabs are (VS, Network, Gallery and Options).