I've never had a client complain that their undercab lights were too bright - go 400 to 500 or higher, but look for a dimmable system so you can turn them down for a dinner party. And be careful with the brand you select. If you go with the cheap ones from Amazon, they produce a green tint to the light. A better brad like WAC has a much whiter light, a better cri, and a lower failure rate. Tresco is another brand - they offer the widest variety in selection, color, lumens, and mounting options. As you plan the system, make sure you can get to everything and replace components if needed. The transformers are the first thing to go, but the leds do have a failure rate as well.

Our drywall starts tomorrow, and our electricians just did the hardwire in 2 locations specified by the cabinet maker. The cabinet guys will fish the rest of the wires for UCL under an upper cabinet and shelf, and inside 1 cabinet. I verified with him, are they really sure that this does not need to be done before drywall, and he assured me that this is how they do it all the time. I asked my cabinet maker to put a flush channel and LEDs right into the bottom of the cabinet, so really all I will see is a strip of light, nothing sticking out. I hope yours works out and you get those lights!

That would be my own preference to keep them united. 3000K is a little easier on the eyes with a yellow cast, 4000K will give you a cleaner, bluer light. You wouldn't need 5000K unless you were running a surgical operating room or something. Design pros are split about recommendations between 3000K and 4000K.

Do your cabinets have molding (example) that is attached to the bottom of the cabinet box to hide any lights and wires you might attach there? If not, I'd use tape lights in a channel as that will be the shallowest solution (hide the required driver inside a cabinet). Otherwise, linkable light bars shallower than the molding would be a good solution. Be sure that whatever solution you choose is dimmable from a wall dimmer. I'd skip the lights under the cabinets. They'll just highlight the dirt on the kitchen floor.