Assuming you're equally skilled at every single Champion you own, I'd say, Heck yeah man, go for playing these champions based on composition. However- that understanding of what is good against who also requires a decent working knowledge of what you're playing against, and who you're playing as---which you'll come to that conclusion on your own.
Instead, I would like to push you to learn two or three of those champions and get really good at them--and then build a foundation of champions that you can play other than those around those. Kassadin is a little out of place right now--he's an assassin, and he can be difficult to play if your positioning is bad.
I would suggest starting with Malzahar as he is a great laner, and will force you to learn positioning as he has no escapes, some CC and some decent damage. Similarly, early game, you will have to learn Mana Management as he does not start with a lot (assuming you do not use your E to farm, and even then, it's not wholly useful until you have an item or two).
Also, Zed is a fantastic option. He's pretty far up there in terms of picks right now, so I would certainly suggest it. Though, often, you should strive to get an AP mid, and this is due to the fact that too much AD on one team IS a thing, and it could lead to a loss if the enemy team counter builds you.
As always,
Good luck and have fun!
-Cap'n Crayon