Well, full disclosure, I'm not that big of an anime guy. I've retroactively tried to get into it in the last few years, but before I turned 27 I'd only watched five anime shows to completion: Gundam Wing, Dragonball Z/GT, Rurouni Kenshin, Ghost in the Shell SAC, and Cowboy Bebop. All dubbed, all on Toonami.
As I now abridge one of those, I've found that I know significantly less about the... well I guess you can't call it "genre" but, like, anime as a whole than most all of our subscribers and followers. So while I've increased my total anime watched to about 15 or so, I'm trying to look back further and get more into "where it started".
For Christmas I found an underpriced DVD set of the original Eva dub and got it, but I'm two discs in and I still don't understand the hype. Asuka just came into things and I admit that her performance so far is the best part of the show, but it has yet to hook me past the animation of the kaiju/robot fights and how I've turned "shots of telephone lines with cicada noises in the background" into a drinking game. (Not really but I swear I'm gonna.)
Sailor Moon I have a vague knowledge of but have never sat down to watch it, and its impact on anime and specifically the "magical girl" genre makes me feel like it's a necessary watch. I also feel like finally watching the OG Gundam is important to my work as a Gundam Wing re-dubber. Know where you come from and all that. So that's why I'm choosing between these three.
Any other suggestions? You seem to know your ****.
In terms of 'general anime' I wouldn't say that I know much more than anyone else who watches it for a hobby. I'd like to think I've seem most of the 'required viewing' titles, a smattering of the older classics and a handful of more obscure titles but I would not presume to be any sort of authority on the subject. Being honest, I'm not too familiar with Sailor Moon either; I've seen a handful of episodes of the 90's anime (both in my youth and later in life) and I think one of the movies. Most of my knowledge that pertains to my previous post comes from reading about the bizarre circumstances of the DiC dub (perhaps the only English anime dub to have a
whole book written about it).
Now 'mecha anime' specifically is a different story, that I am very well versed in (especially Gundam). Evengelion is certainly required viewing for any burgeoning anime fan (those interested in mecha tend to come to it a bit earlier obviously) but the thing to remember is that whilst Evangelion is generally regarded as a classic...it's also an incredibly divisive series and debates over its quality and true influence continue to this day. The important thing is to see it to acquire an informed opinion on the series...even if it's a negative one. I don't know how much of a Gundam fan you consider yourself if your only real exposure to the franchise is Gundam Wing, but I can say as a very committed Gundam fan (who has spent many years interacting with other fans online) that (western) Gundam fans tend to (with astonishing regularity) find Evangelion to be rather overrated or even downright bad. So if you do find yourself disliking the series you may find yourself in good company.
Speaking personally on the matter of NGE: I find the first 19 episodes of the series to be nigh flawless...I don't have any real complaints towards the series up to that point. It's everything after episode 19 (episodes 20-26 + End of Evangelion) that tends to be the 'make or break it' part for most people. Eva post episode 19 is an undeniable mess (brought about by a lack of planning, lack of budget and the mental breakdown of its director, plus a whole host of other factors) but whether it's a fascinating mess that allows the series to plunder new depths of characterisation, psychology and philosophy, all wrapped up in an impressive audio-visual feast...or a self-indulgent slog that squanders its characters and plot points and isn't half as clever as it thinks it is...is something that each individual viewer has to decide for themselves. In my opinion, while I wouldn't want to imply that both viewpoints don't have merit...I personally would lean towards the latter as my personal viewpoint; I find Evangelion to be very overrated on the whole. As an addendum I will tentatively recommend Eva's manga adaptation as something to look into after finishing the anime. In my opinion it's the best interpretation of the story and goes out of its way to correct most of the more prominent issues the series had.
As for Gundam, well watching the original is a great idea no matter how you go about, but speaking as a very knowledgeable fan I would strongly advise watching the compilation films over the TV series. Many anime fans I know tend to baulk at such a suggestion having long been conditioned into finding compilation films to be cheap cash-grabs which end up being vastly inferior to the series they're complied from, and in general they're not wrong but the original Gundam's film trilogy is the ultimate exception. Most Gundam fans broadly agree it to be better than the TV series and
especially better for new watchers as the films cut most of the weaker episodes and goofier stuff while retaining all the important parts of the narrative and improving them with sprinkles of higher quality animation. If the TV series is the only convenient way for you to watch the original Gundam then go for it, both versions are fantastic but do watch the film trilogy if at all possible.
If you want to learn more about Gundam I would also recommend Gundam's first full length sequel 'Zeta Gundam' (50 episodes, 1985) which is broadly agreed to be the best Gundam series, or at least the benchmark from which all subsequent Gundam series are measured. A word of warning however: both the original Gundam and Zeta Gundam are very different in style, execution and overall tone than what you may be used to from Gundam Wing. A more familiar Gundam I will kick in your direction is 'Gundam 00' (50 episodes + movie, 2007), an (in my opinion) excellent series that whilst to call it a 'spiritual successor' to Gundam Wing would be going too far, certainly had aspects of Wing in mind during conception and it might be a good place else to look in the Gundam franchise if you want more familiar footing.