Being I have not got this done yet I will start a quick list off the top of my head.
These are items I carry into the home. Other tools that I don't need to carry in with me every time stay in the truck.
Infrared Thermometer (sears special I bought years ago)
Snap on ratcheting screwdriver with 2 square drive bits, 3 star bits, #2 philips bit and 1 standard straight bit.
1/4 inch drive ratchet handle with 1/4, 5/16, 3/8 deep socket, 7/16 deep socket, 1/2 deep socket.Combonation Gear Wrenchs
1/4, 5/6, 3/8, 7/16, 1/2 inch.
I really like the gearwrenchs. I have had this set for years except for the 1/4 gearwrench that I just got a few years ago as they just come out with that size.
Will add to my list of tools some more later as I get more time.
I find that you do not need all that many tools for appliance repair.