LUmens are total light output, and the light output can look quite different depending on the type of beam, even with the same lumens.
A broad floody beam will distribute those lumens over a larger area, so that the overall result is broad, but not as bright as a narrower beam which concentrates its lumens into a smaller area. Same lumens, different results.
You can research the beam types of the lights under consideration, and decide which type of beam would be best for your use.
In general, a fairly floody beam is best for general purpose, but it should have enough intensity to reach a reasonable distance for your purposes too.
Tint is a subjective matter, based on your personal preferences of beam color.
"Cool white" is generally around a beam color temperature around 6000K, and typically has some blue or purple tinge, at least around the edges. The beam center generally looks white, with perhaps a slight ice blue look, but not much.
"Neutral" is generally between 4500k and 5000k, and looks a bit creamy ivory at 5000k, and starts getting a yellow/brown/peach tinge to the color, at least around the edges.
"Warm" is generally under 4000k color temp, and this is a quite yellow/brown/peach type color which influences the entire beam, right down to the center. You have to really like this kind of color to want a light that is "warm". It's sort of like the old incandescent lights that cast that kind of color.
"High CRI" is an accurate rendition of colors, and it normally comes in the Neutral or Warm color categories. It makes the colors of things you look at appear to be more natural across the spectrum. It especially helps the yellows and reds which are inherently weak in the normal LED light output.
The "warmer" that you go in beam tint, the lower the actual lumen output of the light will be. They have to coat the LED with phosphor coatings to get these warmer tints, and that reduces the brightness by up to 25%-40%, depending on how "warm" the tint is made to be. The battery power used is not reduced, however. It still uses up the battery at the same rate as the "cool" version which gives more output. So, there is a price to pay for these "warmer" tints, by way of reduced output at the same battery usage.