For most of us, there is no avoiding pest problems. What is often not understood is that plant pests thrive on plants that are under stress for other reasons, including improper light and water. Sometimes pests keep coming back because the underlining stressors are still present.
The key to safely and effectively treating most plant pest problems is making direct contact will all of the critters, including the juveniles that are virtually invisible to the naked eye. Treating only what you see, is not effective. For mealybugs, mix a solution of 5 parts water, 1 part alcohol and a squirt of liquid dish soap and then spray the ENTIRE plant until all leaves and stems are dripping wet. This is a messy task and best done outside. But if you are thorough, it is usually effective and will not require re-treatment.