It was a while ago but I think I started watching sailor moon, pokemon and yugioh all about the same time...as for what came first...we will never know. :P
the first one i watched was pokemon but i was too little to understand what happened.
hayao miyazaki´s movies like totoro and kiki was also some of the first ones too.
the first one i could understand was dragon ball z..nyaa i only watched some of the episodes (since love the manga, but i´m not really into the anime) so yeah..
the first whole anime i saw was "say i love you"..
long and weird answer (sorry i´m so bad at english, probably made like 100 fault´s...SORRY!!)
Ouran High School Host Club. I watched Mew Mew Power, Dinosaur King, and Magical DoReMi when I was really young, but that was with 4Kids so I don't really count them as my "first" anime.
well i guess it was pokemon... but inuyasha was the one which brought me into the anime world! to be frank ive not known that pokemon was an anime b4 i joined this club