What is the best type flashlight and best brand battery?

The "best" flashlight is a highly subjective term.

What task do you want it to be that best at performing? Those 20-cell Maglites are good for lighting something up, but it does you no good if you left that light in your vehicle and you need it inside the building RIGHT NOW. In this example, a mini-Maglite that you carry in a belt holster on your person is a MUCH better light. Why? Because you have it when you need it.

I prefer a Fenix LD09. It's advertised at 130 lumens and uses 1 AA battery. Yep, that is small enough to fit into my jeans pocket and I can always have it with me.

Additionally, I prefer Sanyo Eneloop batteries (rechargeable) with a Sony Smart Charger. Unfortunately, Sanyo sold the Eneloop brand to Panasonic, who is continuing to market the Eneloops. Time will tell if they are as good as the original Eneloops.

Lastly, for C and D-cell flashights, I have inserts that allow you to use 1 AA battery in place of 1 C or D battery. That turns a 4 D Maglite into a 4 AA Maglite. What is the benefit? For me, it allows me to use my rechargeable AA Eneloops in the larger lights at no additional costs, I do not have to keep multiple sizes of batteries, and you do not loose any brightness.