I'd probably skip the Home Essentials kit and just get a set of drill bits. Most of the other things in the kit are also covered in the tool kit.
I also like to have a set of tongue and groove joint pliers (Channellocks) around as well as a little kit with electrical connectors/tape/wire. I have a kit similar to the tool kit you listed except it is Harbor Freight and I have n a small tool bag containing the few extra items above as well as some duct tape, flashlight (can never have too many), mechanic's gloves, and a small multimeter. I haven't run across any repair I haven't been able to do yet.