I would like an anime that has humor, convincing handwaving, good suspension of disbelief, space that actually makes sense, plausible physics and as few cases as possible of bad research.
I dare you to find one.
Then don't watch
Gantz, even tho it frakkin rulz.
Wow, best hard core sci-fi anime with semi-real physics.....tough one! Star Trek and Stargate like shows are out, cuz they are terrible as far as their science, even tho they are a blast to watch. I would have to also recommend Ghost in the Shell TV series. Great science, with a whole lot of "what does this science mean" when extrapolated to its effects on the human society as a whole. Also, best space combat ever in Anime (IMHO), is Starship Operators. Sadly, very few episodes, but it used some real sci-fi fiction physics standards (based on the approximately 100 + books of the stuff I have read at least) for its combat physics (ie, no ships shooting phasers at warp speeds blah blah blah). Its More like, "Holy shit captian, were are moving at .6c, the enemy is moving at .5c, our closing velocities are nearly incomprehensible. Our attack envelope is .001344 seconds long at that speed. It will take us 2 days to reduce velocity and turn around to chase them! What do we do!!!!"
but, also, cowboy bebop is good......actually, its brilliant and the music is outstanding.
if you want really good story and just plain scary, try "When they Cry".
Also, hellsing is good, but Hellsing unlimited is MUCH BETTER.
Avoid anything with Giant Robots, cuz, IMHO, they are a crutch for bad storytelling, unless its the original Gundam.
Also, the classics that really got Americans hooked:
Vampire Hunter D
Akira
Bubble Gum Crisis (cheesy, but really really fun)
EDIT:
NINJA SCROLL (jeez, how could i have forgotten Jubei!)
or just watch some Ralph Bakshi films, although they tend to range from R to X ratings.
just ideas and my humble opinions..........
GMcG