Warm, Cool, Neutral, is the kelvin temperature of the color of the light. The lower the temperature the "warmer" it is. As it increases it gets "cooler" until it is a blue color. ~1000k is red, like the sun just before it sets, and as the temperature goes up it gets to orange, then a yellow, ~3500k is a nice lighter yellow that most consider warm. ~43-4500k is neutral, meaning it is almost a white, it is right where the color starts switching from yellow to blue. Most lights in the ~6000k range are considered cool.
Most people like warm and neutral lights because they make the colors of the object you are shining them on more true to what they are. But CRI (color rendering index) also has an effect on this, but let's stick to just the kelvin temp. With a neutral light it won't really change the look much, they should be pretty close to what they are in natural light. With a warm light, it's like what stuff would look like by a campfire/candle, that nice warm/glowy color. A cool light imparts a lighter tone of the colors on everything from my experience.
So long story short, if it was me getting the light I would probably get the neutral or warm. I don't like cool lights in flashlights, warm is nice, it reminds me/is similar to incandescent flashlights (like a maglite, or any with a bulb). Hopefully that was helpful, and hopefully I didn't mix anything up, it is late hehe!