I've played a lot of sci-fi RPGs over the years, so as others have pointed out, you've got a lot to choose from on the upside.
I've played: Star Frontiers, Traveller, GURPS, Alternity, SpaceMaster, Trinity, Star Wars (WEG), Blue Planet
On the downside, a lot of sci-fi RPGs have specific setting buy-in required or you're doing a lot of work to do your own conversion. Sci-Fi settings tend to be a bit more specific, there aren't as many "genre norms" like there are with fantasy RPGs. So if the setting, really grabs you, pick the rules set that goes with that setting. I had successful campaigns using Star Frontiers & Alternity and have played in successful Traveller games.
Games like GURPS are good in that they give you the crunch and fiddly-bits to develop your own settings if none of the pre-published ones grab you. The downside is, I want to spend more time developing characters, plots, and locales than creating alien species and vehicles. (And for the GURPSians that say, "hand wave that stuff" - if that detail isn't important to me, I'm not playing GURPS in the first place.)
While I'm definitely in my "honeymoon phase" with the game, my recommendation would be Savage Worlds. The Sci-Fi companion isn't even out yet (it's out in PDF next week) but you can easily run a sci-fi game with just the core rulebook. I did a sci-fi survival horror one-shot over the holidays and it was a resounding success. There is enough crunch customization to tweak things to suit your setting desires but it's not so overwhelming that you're spending a lot of time doing it or forced to go with "what the system offers" like you are with most other RPGs.
My 2nd place recommendation would be Mongoose's Traveller, just b/c of the sheer amount of material available (much in PDF format) that you can probably kit-bash what you want together. You probably won't hit all of your requirements in the Third Imperium default setting, but there are some top-notch 3PPs out there offering setting alternatives that might fit the bill.
So, the short version:
1) Savage Worlds Deluxe + Sci-Fi Companion (which will have blasters, mechs, starship combat, etc.)
2) Mongoose Traveller + 3PP supps to season to taste