On a handyman-ness scale of 1 - KCFDcat, how hard is it to put in new countertops?
Depends on if you have access to buy countertops at contractor price or not.
Typically, the countertop folks come out and take all sorts of measurements with a fancy machine then go back and actually manufacturer the countertop at their shop to exactly fit your space. When I replaced mine, I had about 1/4" change in elevation over the 16' length, so the countertop (quartz in my case) was machined to be slightly thicker on one end so it sat level on the top of the cabinets. From the front and top, you can't tell at all, but behind the bullnose, there is some change in depth so it fits perfectly.
To make a long story short, order countertops directly through the manufacturer (I always use Top Master, Inc out of KC) and not Lowes, Home Depot, etc. You'll get a much better price and service.