What got me into Anime was watching it on Channel 4 and the Sci-Fi channel.
Watching Guyver (The OVA series) and flims like Cyber City Oedo 808, Battle Angel, Dominion Tank Police, Fist of the North Star and Akira and many others I guess. Guyver was and is really only Anime series I ever collected, I have the full 12 episodes on VHS in the loft somewhere. They don't make Anime like they did in the late 80's and 90's anymore, not to say some of the current stuff isn't awesome, but back then a lot of the shows was gritty and dark.
But it's only the last 5+ or more years when I had a PC where I really been able to get into Anime again.
Pretty much the same here.
The "late license" slot on C4 in the 90's, with 3x3 eyes, legend of the 4 kings etc, then Bubblegum Crisis on Sci-fi, and my (now brother in law) used to invite my younger brother and I round to watch stuff with him - Ghost in the Shell, Blue Sonnet (anyone remember that?), and Psychic Cop (or something similar).
I really got into in about 2000 when not only did I actually have some money to spare to buy anime, but had a computer and the internet so I could actually order it to be delivered easily, including from abroad.