Doubt that a single soul on these forums knows of these games since they're about as unknown as Fire Emblem prior to Smash Bros/Awakening but whatever.
Super Robot Wars is a series of Japan-exclusive (excl. 3 games) Turn-Based Strategy RPGs. The theme of the series is that it takes various mecha anime and squashes them together leading to an epic (http://i.imgur.com/ZnfuaJt.png) crossover.
Unfortunately because it's a mass-crossover of licensed characters it's a bit too pricey to localize in the West and so the only 3 games we received have an entirely original cast (and sold like shit so we're not getting anymore).
Now you're not going to find your Gurren Laganns and Evangelions sprinkled around everywhere, each game has different casts and the only actual mainstays are Gundam, Mazinger Z, and Getter Robo (Getter is not in SRW J though.), and because of the fact it's a Japan-exclusive RPG you'll either have to know how to read Japanese or get hold of a translation (and you will probably need to emulate).
The Touhou fan-game series Gensou Shoujo Taisen is based on these games. (I know Touhou is a shitload more well known than SRW.)
Pastebin of English translations (http://pastebin.com/CbSnEQ8s) (has no links so you'll have to go digging)
The series has a little Final Fantasy Syndrome so it doesn't really matter what ones you play in order (except for Alpha, OG, and Z series.) and actually made an appearance in Project X Zone.
Personally I'd advise starting with either SRW J or Alpha Gaiden. @G is harder than J but is considered a better game while J is easier (both to play and to emulate).
The menus do tend to stay mostly the same between games so it's just a case of memorizing menus/katakana, having a plot guide (if you care, usually on GameFAQs by MNeidengard), having the SRW player's Holy Bible Akurasu (http://akurasu.net/wiki/Super_Robot_Wars) handy, and some good ol' fashioned trial and error.
Screenshots (large warning):
(http://i.imgur.com/ECiTwnk.png) (http://i.imgur.com/Sc5MuNy.png)
Super Robot Wars Alpha Gaiden (PSX)
(http://i.imgur.com/uhGcoaD.png)
Super Robot Wars R (GBA)Could've sworn I took another R screenshot but whatever.
(http://i.imgur.com/AtzHQmE.jpg)(http://i.imgur.com/rBrjueU.jpg)
Super Robot Wars Z2 Hakai Hen (PSP)
Videos: Alpha Gaiden (https://www.youtube.com/watch?v=wcyQHm7954I) | Z3 Trailer (Also SRW 1 HD at the end) (https://www.youtube.com/watch?v=BfnzGB0OlzE)