Hahaha, don't feel bad about not knowing much of a lot of the current anime. XD I think Bear and I are kinda in the same situation.
I recognize a lot of the anime on your list, not because of toonami, but because a lot of them were big hits in the late 90's/early 2000's, my big anime crazed years. @_@ I really love a number of anime on your list! XD
Bear and I've been trying to find good recent anime to watch over the past year or so and have come across some good ones too, but sometimes it can be kinda hard to find anime that you can synch up with since due to the internet allowing a lot more anime to be known about overseas.
Some of the ones we like from over the past year (in no particular order) include:
Samurai Flamenco
Sword Art Online
Hajime no Ippo: Rising (we've been into this series for years. =3 You should really see the older seasons too! >.<)
Kill la Kill
Attack on Titan
SNAFU
We've also been watching Space Dandy which... is really weird and I think really needs some getting used to before you can get into it (IF you can get into it.) The creator is the same guy behind Cowboy Bebop and Samurai Champloo, it has high budget animation too. If you decide to watch this, remember to not take anything that happens in the anime seriously.
umm...
as for older anime that I highly recommend:
Hajime no Ippo
One Piece
Golden Boy
Kino's Journey
Escaflowne
Gurren Lagann
There's probably a lot more I can list, but I should really get going. =)