I don't read manga, but I do know that if it has Go Nagai's name on it the read is worth it even if it'll give you nightmares. For anime I will not be using some I've seen in too many recommendation topics that aren't worth the time (IE FLCL, TV Nadia, TV Nadesico, Rayearth, Macross Plus, Gundam 0080, Black Lagoon, Mai-Hime, Cardcaptor Sakura, Golden Boy, Vandread's first series, any incarnation of Patlabor that isn't the third movie, Otaku no Video, Chobits, Girls und Panzer, Casshern Sins, Watamote, Dream Hunter Rem, Madoka Magica, etc). Just as a quick warning being "beginner friendly" is not something that applies to all good anime.
-Macross Zero: A good introductory entry into the Macross franchise as it is the first in the timeline and is very standalone. For its time the CGI was top notch and it has a good soundtrack going for it. Just don't expect a happy ending. This was originally set to have a US release, but got cancelled for no reason.
-Detonator Orgun: A three episode OVA series from the master of shading and animation Masami Obari. Very high octane pulse pounding action and thrills, unexpected twists, manliness surrounding the atmosphere, and a final battle worthy of the hall of fame. Was even released with a dub.
-Neo Human Casshern: The original 70s classic, not the over-emo remake shlock. Very dark writing (with episodes written by the legendary Yoshiyuki Tomino himself), lots of action, well rounded cast, and if you like the style of old vintage comicbooks this is for you. Discotek Media recently gave this a US release and it is on Hulu.
-Six God Combination God Mars: 64 episodes and most of the action is stock footage, but the drama and music are really good and it has the best villain in anime history voiced by the same guy that did the Great Leader from the Kamen Rider franchise. The TV series can be found on Hulu in its entirety.
-Zegapain: Mecha anime with The Matrix? It works surprisingly good. If you can tolerate the music and don't expect amazing villains I'd definitely recommend this to anyone, pretty much everything else about it is very well constructed including the romance complete with a very satisfying payoff (which is actually quite rare in anime). Plus Zegapain Altair is the best anime robot of all time.
-Death Note: It is one of the best and everything it does is executed extremely well, I can't do it justice.
-Fang of The Sun Dougram: If you can stomach 75 episodes and like military and political oriented drama with mecha than this is a must see. Despite being dated this was surprisingly very compelling with everything plotted out properly with very good world building and an exceptionally good cast to boot.
-Nobunaga The Fool: More for people that like theatrics, but if you're into serious drama and don't mind everyone named after historical figures then see this ASAP. Without a doubt it is the best anime of the current decade with writing, visuals, action, pacing, and characters made by the legendary Shoji Kawamori himself with music from the greatness that is JAM Project.
-Gundam SEED and Destiny: Does stock footage bother you? What about 100 episodes in length? Not okay with protagonist switching? If you answered no to all three of those questions then repare yourself for the best Gundam timeline to date and I say this as someone that has seen the entire franchise. Everything about it is top notch for its time even if some visuals have not dated so well; I'd recommend seeing the original versions over HD if you have the option.
-Victory Gundam: Best of the Universal Century gundam timeline and very standalone filled with very dark atmosphere and writing with great pacing action plus adventure. I dare go far as to say this was Tomino's best television series.
-Space Runaway Ideon: Very similar to Victory Gundam, but with more focus on adventure than the grit darkness. For the time the visuals were quite amazing and it gives off an atmosphere or lurking horror from the great unknown. The TV series was concluded in a pair of movies.
-After War Gundam X: An alternate universe version of Victory Gundam; it has a lighter tone compared to most gundam entries, but it makes up with it by having a better cast and amazingly great music.
-Anything with Getter Robo in the title: The original 1974 series, the sequel from 1975, Armageddon, Shin vs. Neo, and New. I can't do them justice, they are simply too manly.
-Anything that Go Nagai's name is listed: He is the best person in the anime industry of all time. Bar none. You can't go wrong with him. After you have seen enough you will have witnessed the essence of manliness itself.
-Brave of The Sun Fighbird: Best entry of the Braves franchise featuring great heroes, superb villains, amazing action, well crafted music and visuals, and a final battle worthy of makings its mark in anime history.
-Brave of Legend Da-Garn: Most of the same reasoning as Fighbird except the protagonists are not as good. However, it does portray its villains as exceptionally intelligent for anime standards with some clever writing. Keep in mind this was made with environmental messages as the theme, but it does it extremely well. Just don't expect subtlety.
-Zoids: The original 67 episode series, if dated CGI does not bother you then there will be plenty of action and adventure to satisfy you.
-Genesis of Aquarion: My favorite standard anime of all time (I say standard because by technical standards is the best anime of all time and the only one I can unquestionably call art). 26 episodes and a 2 part OVA tie-in. It is art. Every category flies with passing colors. Everything within its mythos and story is drenched in mythology of the Eastern civilizations of old and now. It goes above and beyond, regardless of what impression the audience has, to achieve its messages and strides on the idea that as human beings one must not walk alone nor must the past dictate our future. Nobody is ever useless and in combination great achievements can be accomplish that will resonate throughout history.
Then EVOL was made and made the original series look like a joke.

Sadly it never recaptured what made Genesis so grandiose despite superior production values including the best opening theme in anime history. I'd recommend EVOL as well if not for people crying about how the main heroine fits more in the 1950s than today (yes because showing mercy to someone is such a BAD thing).
I have more recommendations I will post later.