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.