You can certainly do it yourself. They make coil cleaner in spray cans that foam up and are non-corrosive and self rinsing. An HVAC supply house like Johnstone or R.E. Micheal will have it and should sell it to the general public. Home depot and Lowes don't normally carry the good stuff.
If you have a caked layer of debris, manual removal is necessary.
Grab a can or 3. A 1/4 & 5/16 socket for the drill. Remove cover plates, spray with unit off. Let dwell.
You can take a spray bottle of water with you to rinse it off even more. While you are rinsing the coil, dump water in the evap pan and see if it's all draining out properly. If not, then your unit isn't positioned correctly.
They make tablets you place in the drain pan of the evaporator to help with mildew buildup and to help with keeping your drain line clear. They can last about 4-6 months.
Ballpark price? Probably 1 to 1.5 hour of service. ~$100-$175.