Let's see, alot of stuff I like is already mentioned here.
I see you like giant mechs, I would recommend Super Robot Taisen if you know Japanese.
I don't know Jap but I play for the gameplay and good smooth animations of Japanese anime robots fighting with beam swords, bullets, wave motion cannons, and whatever mystical weaponry their respective series use.
To start you off, I would say play the PSP ones because they're menu patched and arguably the most pretty ones with English available.
An upcoming localized PSP SRPG is Summon Night 5, coming out on the 15th. It's very story heavy though (like visual novel heavy).
For Fire Emblem, if you don't have a 3DS, I recommend Fire Emblem 12: New Mystery of the Emblem - Heroes of Shadow and Light (Remake of FE 3 on the DS).
It has a full English patch and it is the first FE game to offer Casual/No Permadeath mode.
It's also the first game with a playable tactician (like Avatar). It's called My Unit in this game and he's the Hero of Shadow supporting Marth, the undeniable Hero of Light.