Depends!
With a light for your keychain, my priorities go this way:
1. battery type
2. size
3. output
4. runtime
5. throw
I prefer an Arc AAA for it's battery type, size and output.
My minimag running a high binned R2H luxeon at 1.65 watts has other priorities.
1. Output
2. battery type (NiMH AAs)
3. size
4. throw
5. runtime
The second R2H I have is on my bicycle helmet for riding at night:
1. Output
2. Throw
3. Size
4. runtime
5. battery type
The R2H Mag 2D that runs at 2.4 watts and is my frame mounted bike light has slightly different priorities
1. Throw
2. Runtime
3. Output
4. Battery type
5. Size
Generally, I use 4 flashlights everyday, two of them are the lighting system for my recumbent (cops love my lights) My other lights are for camping, deploying to other countries around the world, lighting for magnifying optics and backup spares.
As you can tell, it all depends on what your needs are. My batteries are NiMH AA and D cells and alkaline AAA and D cells. Imagine burning lights for a bicycle 5-7 hours a week with three lithiums in a Surefire... Can't get lithiums overseas easily so for my needs, battery type is critical in all my lighting uses.
Welcome to the CPF, just know that your wallet will grow gradually thinner as time presses on. Enjoy!