For your cell phone, I suggest getting a car charger—probably more efficient, almost certainly so if that's the only thing you're using on the inverter. The inverter takes in DC power from your batteries (which are charged by the solar panels, perhaps among other power sources) and transforms it into 120V AC power for household devices.
Microwave and electric coffee maker are big, big power consumers relatively speaking. Without a substantial (and physically large) battery bank, you won't be able to run them well, at least for any very useful length of time. A small immersion heater of around 150-300 watts will heat a cup of water in a few minutes and is readily powered by a small inverter. (A propane stovetop will also heat water and make coffee quite handily, of course, and requires no electrical power.)
You can look on the power brick for the laptop for its consumption; mine is labeled as producing 170W (its output) and has a maximum input current listed as 2.5A. Apparently the power factor isn't as high as one would prefer. At any rate, a 300W or 400W inverter would power it readily.