Should I get an air sprung or a coil sprung rear shock FS mountain bike? I have not bought one yet, and I am very new to the sport. The type of riding I will be doing is dirt jumps (rather large ones) and rugged trail riding. I used a BMX for these things previously, which actually worked out pretty well. As a newbie to the sport, I am just wondering: which type of rear shock would be best to look for: air, or coil?

I want something that is going to be easiest to maintain, and most efficient while riding. A bike I have been looking at is the Scott Voltage FR 30/20/10 models (these all have a spring rear shock) or a Trek Slash 9/8/7 model (which have a hydraulic type shock). I am leaning towards the Scott Voltage bikes, they look simpler, but I am unsure.
You're mixing up two different concepts.

The damper, which is what slows things down.
The spring, which is what holds the weight and absorbs shocks.

The damper is usually hydraulic, oil being forced through a small hole.
The spring is either a coil or pressurised air.

Without a damper, you'll have a very bouncy ride and without a spring, you'll have a very stiff ride. The 2 work together to provide a nice ride.

Also, those 2 bikes target different styles of riding.

The Slash is an Enduro bike and the Voltage a Freeride bike.