I know "Ghost in the Shell" is highly acclaimed so I'll see if Netflix has that available.
You're in for a cybernetic treat.

Just make sure you watch it in Japanese with subtitles. I can't stand dubs, some random voice actor always ruins it with a cheesy performance(that goes for all anime but that's my own personal bias I understand some people can't stand reading subs). Another one you might want to try is "Cowboy Bebop". It seems to do as well with western audiences as Ghost in the Shell.
... that "moe" crap became the norm in Japanese animation.
What's moe, T&A?
And recommendations, would those be Akira, Spirited Away and any other from Studio Ghibli?
Moe Fan Service(T&A = tits and ass) I'm not a big fan of Akira like some people are. I find it kind of plodding plot-wise, but I do recognize the impact it had here in the states when it hit back in the 80s. And the Ghibli stuff, while amazing(really beautifully done), aren't sci-fi so not exactly among my favorite titles of all time.
A couple of my personal favorites that I can recommend to a hard core sci-fi fan would be:
Votoms- Part Blade Runner, part Mad Max, part Star Wars and totally awesome! Might be hard for someone who doesn't pirate to get it all because many of the releases in the series have only had fansub releases(no commercial release).
Macross- Sci-fi with heart. The only release in the series I don't care for is Macross 7. The first release (Super Dimension Fortress Macross) is a classic and a must-watch imo.
Gundam- The franchise that gave birth to the "real robot" genre. I rarely recommend the original series for newbies because it's got kind of a "monster-of-the-week" format which some people don't like, but it is the classic. If you want to dip your toes into the Gundam waters try an OVA or two. My personal favorite OVA is "O8th MS Team". My all time favorite Gundam show is "Gundam X", but I seem to be in the minority on that opinion.

If you prefer something a little more recent yet not quite sci-fi in the traditional sense(still have mechs but the theme is hardly sci-fi):
Samurai 7- Anime interpretation of Seven Samurai. Amazing show.
Code Geass- Probably the best anime to be released in the last decade. Twists and turns that will keep you on the edge of your seat!