How to minimise exposure to systemic pesticides while eating non-organic fruits and vegetables?

You reduce your chances of consuming pesticides by looking at the country of origin. For example, EU countries frequently have tighter standards than Asian countries, and even within the EU, there are differences in which pesticides are allowed, and at which levels. You would have to find out whose regulation you trust most, and then follow the relevant magazines about potential contamination/limit excess reveals.

This is usually in direct contradiction to your desire to spend less on produce, since the norms tend to be better in countries with higher labor costs, conformity is better in countries with low corruption, which also have a correlation with labor costs, and in general, it is impossible to keep low produce production costs without generous amounts of strong pesticides, because the farmer then has to absorb the losses from ruined crops. So if you can only afford the cheapest tier of produce, such as Spanish strawberries, there may be nothing you can do but eat it with whatever pesticides it contains.

What can also help is eating seasonal produce. Out-of-season produce is frequently delivered by mass producing, purely profit-oriented corporations who trim their production to efficiency. Smaller, traditional, more idealistic farmers tend to grow in-season, and even if they don't get an organic certification, some of them would reduce their pesticide use based on personal beliefs what farming is about. So on average, you will have a somewhat lower pesticide exposure, even though the actual levels will vary wildly per batch.

Devils advocate comment: Certified Organic foods give zero guarantee of being pesticide or herbicide free. Organic certification limits which chemicals can be used, not if any can be, and commercially produced produce marketed as organic will use those materials systematically just as non-organically grown will use theirs. The basic rule is that for organic, the pesticide, herbicide, fungicide or fertilizer has to be from an grown or mined source, not a refined source and some of the approved sources are not that nice or harmless.

To directly answer your question, well, it really is hard to say. I have never seen a reason to use a chemical on things like squash or pumpkins, and yet I know commercially they do. I for years though citrus was relatively chemical free, but was told recently this is not true, than many have insect issues and use systemic pesticides. I personally would recommend trying for local grown farmers markets or small farmers and freezing/canning but that is also not cheap and still might be iffy unless you get to know and trust the growers because if a small grower does use the chemicals, they may actually not stay down to recommended levels.

However, this list comes from a Dr. Mercola. I make no claims to his accuracy, but he quotes an "Environmental Working Group" using USDA data to claim the most contaminated 12 are Strawberries, Apples, Nectarines, Peaches, Celery, Grapes, Cherries, Spinach, Tomatoes, Sweet bell peppers, Cherry tomatoes, Cucumbers in that order. The 15 "cleanest" were Avocados, Sweet corn, Pineapples, Cabbage, Sweet peas (frozen), Onions, Asparagus, Mangos, Papayas, Kiwifruit, Eggplant, Honeydew melon, Grapefruit, Cantaloupe, Cauliflower. You can see more here but that was also a limited study with their own criteria.