Re: Best Mecha rpg
The Robotech rpg (both old and new editions) uses the Palladium system (or at least a close enough iteration that differences aren't worth mentioning), and if you're familiar with the system you'll know if that's a good or bad thing depending on your own preferences. If you're not familiar with it, then you might want to look into it or start a separate discussion.
If you want a game set in the Robotech setting they make great source books even if you run using another system.
Mekton Zeta/Mekton Zeta Plus run using the Fuzion system. It's a pretty universal mecha game so you can do a lot of types of genres with it. Plodding Battletech style mechs, transforming Robotech styles, and even Sentai type combiners. The base Mekton Zeta game is a full game, but Mekton Zeta Plus cranks up a lot of the crunch factor with a lot of options for building your custom mecha. The system can be numbers intensive, especially if you get into custom mecha designs and the like but the many years ago that I played it, I remember it running fairly well. It'll do your space opera oriented mecha game fairly well as I think there's some rule for spaceships and such in one of the books if they're to matter more than as a backdrop.
They Kickstarted an updated version of Mekton somewhat recently but it's still in production I believe. However the original games are still available for sale in pdf.
There's the Mecha rpg, by Chris Perrin. I've never had the chance to play it but it looks interesting with mechanics that seem somewhat streamlined and some story gaming elements.
I'm sure there's a couple more specific games I've heard of that I'm simply forgetting about. There's also the universal systems that can run Mecha games (Gurps, Hero, etc).