Lets see my first anime. Well in all truth it was probably Maison Ikkoku, or KOR. The first one that caught my attention though, as far as I remember (or want to remember) was Ah! My Goddess. Way back when George started me on my path to all of this crazy stuff.
As for my first manga, that takes a little more thinking. I'll not add why it takes much thinking as it would scare the children.
I think one of the Sailor Moon mangas was the first that I ever owned, though that was originally to give to my sister. When I started getting lots of manga (before the lack of money and need to eat kicked in) Ah! My Goddess, Ai Yori Aoshi, and Maison Ikkoku were probably in the first purchase. Now of course I only buy Ah! My Goddess and waste all of the rest of my money on take out. It will be worth it though. One day I too will get a wrong number, and then I will be hung up on almost immediately.
I'll throw in Tobor the 8 Man as my fathers first, just because that show is great.