How to design a top-1 select algorithm to maximize a variable and minimize other variable?
This question is not answerable.  Only you can tell us what counts as a good tradeoff, for you.  You need to pick a single objective function that combines A and B into a single quantity.  We can't tell you how to do that, because that will depend on what makes sense for your particular application domain.

For instance, maybe it's best to choose the item with the highest value of $A/B$.  Or maybe it's best to choose the item with highest value of $A-B$.  Or maybe its' best to choose the item with highest value of $100A-B$, or $A-100B$, or $A + 1/B$, or $100A + 1/B$.  We can't tell you.  You will need to analyze your application to determine what the right objective function is.  Take a look at your specific application and understand what is a measure of benefit or cost that is meaningful in your application domain, and then figure out how that depends on $A$ and $B$ ... and use that as the objective function to maximize.