I think mine would have been something like dragonball in the early 90's but I was probably too young to know what i was looking at. and of course all the morning TV cartoons before school like pokemon and dragonball z, cardcaptor sakura, sailor moon and all of that stuff.
The first proper anime I watched would probably have been Evangelion as an edgy tween.
The first anime I ever watched was Pokemon, but I don't really count that, as I had never even heard of the word "anime" back then.
My actual first was Mahou Shoujo Madoka Magica. It's still one of my favourites to this day.