For Ranger School, you are required to bring eight AA and/or AAA batteries, but I would bring at least twelve AA and twelve AAA. Ranger School is mostly in the field and you don't want to run short on batteries.
For Sapper Leader Course, you are required to bring a minimum of 20 AA and/or AAA batteries. You need enough to sustain your NVGs, headlamp and flashlight for the ten day FTX.
For SFAS, you are required to bring twelve AA and/or AAA batteries.
As far as Alkaline vs. Lithium goes, I went with Alkaline when I attended these courses because they are cheaper and you will replace them regularly anyways at these courses. The last thing you want is for your headlamp or NVGs to die on you because you didn't put fresh batteries in it before you stepped off.