What inspections/maintenance should be done before first air conditioning of summer?
The pan tablets are to prevent gunkies from growing. You do not want to be checking freon levels unless your system has a site glass. Then watching for bubbles in the glass, some fully charged systems will have bubbles. The reason you don't want to check pressures that requires opening the system and a small amount of freon is lost. HVAC techs use special sealing compounds on the threads and instruments to verify there are no leaks at the end of a service (I and the guys I have worked with do anyway). There are special gauges used for testing the high and low side pressure, the type of freon and temperature are all used to determine if the system is properly charged. 
Really the only thing you can or should do is; Clean the outside condenser coil. Clean the inside evaporator coil. Verify the insulation is in good shape. Possibly add a few drops of oil to the fan motors. Install fresh air filters and keep the condensing coil drip pan clean.