The secret to keeping pests down is native plants. In the mid-Atlantic: My uncle's garden is lined with marigolds (which keeps down nematodes that attack the roots of your vegetable plants). Nasturtium keeps down the aphids (and is fully edible). He also plants "companion" plants that attract bees, wasps, ladybugs, and butterflies. All bugs who benefit the garden in a number of ways. (You can buy and infest your garden with ladybugs as well. Make them a nice home and drop them in at night and they'll usually camp out for a few weeks. If they really like it and stay then you're golden.)
Companion gardening is actually how agriculture worked for thousands of years before genetic engineering came along. It's also how nature works. We do this for our container gardening as well. Everything we grow that may be susceptible to pests has a container next to it growing a companion plant. We've had great luck with Pelargonium citrosum, which is a citronella-scented geranium. We've tried and failed with citronella proper, but the broad-leafed geranium really does the trick. It's protected our tomatoes (even from birds) and is the rose bush's best buddy. Our big container rose was plagued by aphids but we jam the citronella around the base and it's aphid free. Chives protect strawberries. Thyme protects everyone. Most companion plants, you'll find, are also edible flowers or herbs.
He's had great success without having to resort to chemical sprays (and the "safe" DIY sprays rarely pay off). So, at the moment, his greatest enemy is rabbits and deer.
Healthy soil is key as well. The first step to this is permanent garden beds. My uncle's raised all his into garden boxes so he can monitor and control soil conditions. You sneak in "pathways" here that can be home to your companion plants and also soil-enriching plants like clover and other ground plants (don't get something super invasive here). Compost these pathways as well.
Before he planted his garden he sheet-mulched the boxes. Cardboard (non-treated, 100% recyclable only) and homemade compost under the soil, sit for several weeks (anywhere from 1-3 months) to let it break down, then plant. This brings in worms and other soil bugs, who are your first line of defense against pests.
If you buy store bought compost or soil, then make sure it's high quality. Usually the packaged stuff is laced with herbicides and pesticides that will set back all of your work. Basically avoid at all costs. For our containers, we buy ridiculously expensive soil (or gather it from the creekside if we're bored) and use our own compost.
Also, just like the thousands of years of agriculture behind all this, you want some boxes to go fallow each year. These you can sheet mulch and plant cover crops (or, better still, companion plants like herbs) to prepare for the following season. Rotating crops also confuses the pests who tend to be very specific if they infest one plant or area of the garden. They'll die off instead of moving to wherever you've moved to.
Also pay attention to sun and shade-loving plants, moist and dry, etc. Never the twin shall meet in the garden. So you'll need sections.
Um...sorry. I study this stuff all the time because I want to move to an armed compound in the mountains.