What they want is unclear. Reclaiming the Russian Empire's breakaway provinces is one possible goal. So is removing a democracy that might inspire discontent with Putin's transition to Czar. Grabbing control of oil and gas pipelines through there would allow much more leverage over Europe. All of the above may be the likeliest answer.
I suspect the NATO negotiations may have been the deciding factor in timing the Russian attack. Putin wants to avoid direct combat with the USA so he's not going to attack an actual NATO member. So Georgia had to be dealt with before it could join. Right now Ukraine has the same "Attack Now Before It's Too Late!" sign hanging on it so we'd better make a decision. Otherwise we're making once again the mistake we did in 1950 when Acheson left Korea out of the list of nations in our "defense perimeter."
The most important decision to make is choosing our grand-strategic goal. The response to the Russion agression follows from that. Do we want to maintain a balance of power? Then we supply Georgian freedom fighters with weapons to bleed the bear and draw a clear line at the borders of current NATO members. Do we want to protect emerging democracies so the world can become a better place? That calls for economic punishment of Russia, providing a NATO troops to Ukraine, and active support of Georgia to help it maintain its independence, if not all its territory. Or we can decide that avoiding dangerous conflicts is our highest priority and issue harsh statements while doing nothing.
I think the world is moving toward a time when we can't tolerate dictatorships. Right now the wars they launch and the terrorists they spawn can only cause a limited amount of damage. But technology is giving both more power to cause damage every year. Eventually there will be an explosion. The more free people in democratic nations we have by then the better the odds of a good outcome will be. So we need to protect democracies now.
Our ability to do that is limited. War with a nation wielding thousands of nukes is not an option. What we can do is expel Russia from the G8 and cut off their liaison access to NATO facilities and exercises. Supplying weapons to Georgia will give them a chance to preserve some of their nation. Stationing troops in Ukraine will draw a line that even Putin will respect.
That all assumes we have protecting democracies as our goal. Right now the US hasn't defined one--the population is too divided and most people haven't considered the issue. If we get very, very lucky the current election may tackle that as an issue. Then we can vote on it and have a decision to base our actions on.