Alpha Centauri is really, really well balanced; any ranking is going to be more a reflection of player tendency than game effectiveness. Moreover, different settings are a lot different in value in different game situations.
That said, I'll give it a shot just to give some things to think about:
1. Efficiency: Efficiency reduces drones when you have a large number of bases, and saves energy when you have a large number of bases. In the late game, Efficiency settings (green, cybernetic, research) also make more energy than Economy settings (eudaimonic, free market, wealth). Efficiency is also the most universally important quality; other attributes gain value when your doing specific things, but efficiency is almost always important.
2. Police: I hardly ever play with a high police rating. Actually, I tend to play with Domai, which almost locks me into Free Market, which means I need to do everything right to get even a -1 Police Rating. But I give Police #2 because when you do play a Police State, Planned, THX-1138-esque society, Police are absolutely critical to stopping drone riots. But if you're playing high efficiency, Punishment Sphere, you have the Telepathic Matrix, or you have Free Market and are careful, it's irrelevant.
3. Research: The one thing that prevents any faction from lapsing into obscurity is Research; superior technology is a great boon that everybody profits from. In the late game it is rare that between diplomacy, probe teams and the optional "spoils of war" rule you aren't able to get tech as fast as your oppenents. It's also possible to have a thriving enough economy by the mid game that you can get around a -4 Research rating and still get a break-through every six turns or so. But in the early game low technology is a killer; as Domai, the thing that really kills me is when I am stuck with Synthmetal Garrison units and am getting monkey raped by Plasma Impact Infantry before I even have probe teams.
4. Planet: Planet is important in the early game only against the little mind warm boils, and typically you can deal with those. Unless the Hot Chick or Cha Dawn starts to assault you with a handful of captured mind worms, which is a scenario that becomes a lot more likely in the mid-game. In the late game, bad planet rating starts to result in Eco-Damage for all your bases, and you start getting mind worm pops every other year that can over-whelm your base defenses. Rarely is Planet the primary concern, but everybody needs to condsider it. If a Gaian or Cult player has the Dream Twister or Neural Amplifer and is playing Green- Cybernetic, then it's primary concern.
5. Morale: It is expensive to use secret projects and base facilities to over-ride a bad morale, but it is definitely possible later in the game. The problem is biggest early in the game when "Very Green" units are getting assaulted by "Veteren" units, and you have neither the technology for base facilities nor the infrastructure to support them. Ms. Deirdre needs to use a whole bunch of "Very Green" scout units to take out the one "Elite" scout that Ms. Santiago sent her way. But if a player got the Cyborg Factory and Cloudbase Acadamy, he's not going to really care. And technology is a much more common factor in late game battles than morale.
6. Growth: Growth is irrevelant for most of the game; there's a long period between Hab Complexes and Hab Domes where you're stuck at +/- 14, depending on your faction. And once you get Hab Domes in the late game, things are so cut-throat you're not really going to concern yourself over growth. But almost every player plans a Population Boom well before Cloning Vats; I always run Planned/ Democracy for a few turns in the beginning of the mid game. If you're stuck at the 8's as a Cyborg and everybody else is at 14-15, you're missing out on a whole lot of productivity.
7. Industry: I love industry; I love pumping out Fusion Planet Busters in the mid-game as Domai- one every 6-8 turns, then a secret project every 10 turns, main battle units every 4, needlejets every 3. Industry has very little impact on anything but production, and it's rare that you see enough of a plus or minus swing that it has more of a bearing on production than any of the other factors; but as Domai, I can show you that getting units for half the price as anybody else is very useful. Only problem is that your monkey-raping me with impact infantry and all I can make are Synthmetal Garrisons.
8. Support: A lot of players use clean reactors to make support irrevelant; after you go through your growth spurt you're not going to really care about support. I've never had a problem with it past the early game. Of course, you might very well find yourself fielding a large army with only limited bases and that might affect your social engineering.
9. Economy: It is under limited circumstances that Economy will make more money than Efficiency; but, when I'm Domai and can't use Green economics, I have to go Free Market to even come close to having enough energy. And there is a small period in the middle game that you'll be filthy rich.
10. Probe: If I'm probing somebody, having bad probe isn't that much of a problem; it is rare that I can't have enough perimiter around my big bases that I can prevent it. However, late in the game all of your outside bases get mind controled and you wish you had probe.
