The code requires 2 separate GFCI 20amp small appliance circuits (for your 4 outlets). A circuit for the dishwasher, and one for the waste disposal (they don't need to be GFCI). You could wire these with 12/3 cable. Don't forget a disconnect (a plug/recaptacle, or a switch). I might be wrong on this, but a dedicated circuit for the microwave (GFCI not required). A circuit for the range (GFCI not required). The only 2 items that don't need a dedicated circuit are the under cabinet lighting which can come from the existing lighting circuit, or add a new one if that is not feasible (GFCI not required). Refrigerator can go onto one of the small appliance circuits (doesn't have to be a GFCI outlet)

You might need to make sure all outlets are 'tamper proof' (depends on you local authority), but at least any 'new' outlets should be.

This is all basic NEC code, and is well explained in various 'wiring' books. If you are unsure about these specific requirements, I suspect you are not familiar with the code and there is a really good chance that you will be in violation in many areas (box fill, wiring methods, ampacity, etc). I would spend the time to read up (it will take a couple of weeks) until you know what needs to be done... or hire an electrician to do it :)

I did not realize that the gas range needs a separate circuit just to run the timer, etc. Bad news.

I mis-read your post, I thought the range was electric :(

The gas range does NOT need its own circuit, if it is for ignition and controls, it can be connected to one of the small appliance circuits, or to a general purpose lighting circuit.

Thanks for the clarification. I am hiring an electrician to put new circuits in my service box, but I plan to run the outlets, etc. myself. I just wanted to be sure I have enough space in the box for all the circuits.