I am going to have to agree and say try and do Space Mountain first. For some reason, people tend to travel Magic Kingdom front to back, and crowds generate to Tomorrow Land for Space Mountain and stay there all day. The Fast Passes tend to run out around 5:00 or so-but in the middle of the summer, when crowds are at their peek, we once saw Fast Passes sell out by 2:00.
What we like to do is stand in line for one ride after getting a fast pass for another. Then after we knock down that ride, we head on over to turn in our Fast Passes.
We are Veterans of Disney as far as summer goes, and I have to say, sometimes I am surprised at how long it takes Splash Mountain to get a line long enough for my sister and I to say, "Nah." But Space Mountains line will have a wait of 75 minutes or more in a matter of an hour or so. Do it first and then head on over to Splash Mountain (Big Thunder is right next door, and you might want to scratch that one off while you're there too, because the lines for that can get pretty long as well!)
Also, I know people will challenge me on this one, but when you hit Space Mountain, if you can, vere off to your left when you get to the "fork" in the line. This track is a little faster because it has some bigger dips and drops.