Before you decide on the flooring you'll want to do a moisture test. Vinyl floor will not allow any water vapor to escape the slab, so as moisture wicks up through the slab it will become wet below the vinyl. This can lead to mold issues and a breakdown of glues and patching compounds. There are plenty of effective ways to deal with a moisture in a slab, but without a test you won't know which to choose.

Now to the question of leveling the concrete, first step is to map out the slab to determine high and low spots. The easiest way to do this is to set up a rotating laser in the middle of the room, be sure it's sitting level and turn it on projecting a level line around the room (the height you set it at doesn't matter). Next take a straight stick, pole, broom handle, whatever as long as its straight, set it next to the laser and place a mark on it where the laser hits it. Then make your way around the room taking note where the laser is hitting the stick in relation to the first mark. Plot several points around the room (the more the better). Marks above the control line means the floor is low, below means high.

High spot are best ground down, low spots are best filled. Most jobs I've done require both grinding and filling. If you find more low spots than high the more leveler you need, more high then low the less you need. Remember to respect all control and expansion joints, and follow the manufacturer's instructions to the tee to insure a proper job.