[Jeopar]

I would suggest "Wise Man's Grandchild"and "Accel World" both are short anime, fast paced and fun to watch.

[Stillski]

God of High-school would be a good choice.

[Maality]

I would suggest "Code Geass" it has good twists and mysteries.
Is definitely worth the watch

[Greenleaf]

Law of Ueki, Get backers, Dan Detective school Q would be good start. Good quality anime, with interesting Stories. Could recommend to see this non- mainstream animes.