Anime/Manga - your first time :P

Well, I started with those shows on TV after School, mostly Pokémon or Yu-Gi-Oh.
As I started to play the Pokémon TCG, there were some guys playing a totally different japanese TCG called "Weiß/Schwarz", which i got interested in, that must have been around 2010. Weiß/Schwarz is btw a card game which features a lot of different anime/games, and as they played cards from AngelBeats that was the first anime I ever watched in japanese (with german subs at the time).

After that i started to watch a lot of recommended series, like Clannad, Higurashi, Bakemonogatari, etc., but also some stuff I found on the german subbers websites, think the first ones were To Aru Majutsu no Index, OreImo and Koe de Oshigoto (ye, the later one got me interested in other things...)

And I think I started to only watch english subs with Jigoku Shoujo, as no one did that in german.

Ohwell, I dont know think I have a particuluar taste, maybe more dramatic stuff as Bokurano, Clannad, Rainbow, Tokyo Magnitude and Usagi Drop are rated as "Masterpieces" by me. (Ye I also read the Usagi Drop manga, well... interesting, but that ending felt much too forced...)

Hmm, it was ages ago, can't remember the year anymore. Not counting the usual cartoon stuff (pokemon, digimon etc.), but the first anime that i saw was from TV oddly enough: Magic Knight Rayearth (Only finns get this but Taikasoturit FTW ) blew me away completely and got me pretty much hooked into anime ever since...I still have fond memories of that one. I was sad when the second season ended since it left me waiting for more, and then came the less interesting stuff: Sailor moon with Swedish dubs, Dragonball Z and so on...Sailor moon would have been allright without the awful swedish dubbings but DBZ was never my cup of tea, so it was a looong break (~4 years) for me 'till i got a better internet connection & PC and started watching anime again, i think it was either Lucky star or Hellsing TV version that i watched when i got back into watching anime again.

As far as Mangas go, it took me years to get into them since i just lacked interest in them. I started being somewhat interested in them when Finlandia: Santa Yousei Gakkou was released back in 2012 (Come on, a manga about Finland? What kind of an finn ya are if ya ain't even half-bit curious about it!) It was no masterpiece, but i still enjoyed it enough to start reading some mangas...fast foward to summer's Animecon and then came the insane bombshell that Magic Knight Rayearth would get a finnish manga translation, and i was sold. It took me time, but now i'm running out of bookshelf space! It usualy goes like this nowadays, if i liked the anime and i can get the manga version as well, that's what i do. There's usually some sides in there that haven't been added to the anime adaptation for whatever reasons, and that just adds to the story then

As far as nowadays go, pretty much anything goes as long as it interests me one way or another (Yes, i have survived Boku no Pico...prob' should do a t-shirt that says that someday), if it's full of bitching & cursing/rape or is a clearly poor copy of a good one, then i usually drop it to the trash bin pretty fast. I was reading VN's way before mangas anyway so even that's nothing new for me either, first VN was Kana - Little sister...oddly enough, can't recall what the second one was.

Well, my reason why my reply was that short because yeah, I suddenly started to feel really old. I also saw Kimba, I watched a lot of episodes with the neighbour sisters when I was around 7 years old or so. As Mila Superstarter, it was in the saturday tv, at the morning, with other cartoons for kids (I actually watched a lot of cartoons). Mila Superstar is actually dubbed in hungarian too, because of this. I remember watching it for more than two years, they aired one episode in every weekend, and I simply liked it. Just for trivia, Mila Superstar was made at 1969. Here is a wiki link for those who are interested: Mila Superstar
I started to watch anime by not accidentally, but with the definite thought of searching them was 19 years ago, and the anime was called Neon Genesis Evangelion, which still one of my biggest favourites. If you look up the wiki, NGE was out around 19 years ago, and it was really hyped. Of course, internet was not like nowadays back that time. You only had a couple of sites, no torrent, no viruses, no stuff like these. You could find anime in FTP servers. Hungary had one, and only one anime community back in those days, and they had a 2 TB capacity FTP server. This was a big word back in those days, because one episode of a 24 minutes anime was maximum 80 MB. At that time, if you put "anime" into search, you most likely got NGE. This is how I found then Ghost in the Shell, and Slayers too. I cherish these too even now (Slayers even got two new series around 3 years ago). 
Those who are interested in older, but good animes, here are the links:

Slayers

Ghost in the Shell

In the old days, animes was very-very different than nowadays. The most powerful way to say it that there were no fanservice, but more story. The sitcoms wasn't centered around ecchi, and overreation.  More like, jokes were witty, or if the anime was about something serious, it had a very good story.