I don't want to paint these issues in purely moral terms. In many ways they're attributable to the increasing complexity of a technological society and the momentum of economic relations. We don't have a good paradigm for self-governance in an increasingly networked society.
The list goes on and on and on for virtually forever. My point is: we work on ALL the problems, simultaneously, as much as possible. There should be no one suggesting that we only try to solve one or two of these at a time.
We will fail to fix some problems, but we will succeed in fixing other problems. And it will only happen because people will throw their hardest try at fixing all of the problems.
We are ahead in many respects: the population in general knows the wide variety of problems that this country has. So we're able to talk about it. So we're at least at step 1. It'd be nice if we could come to consensus faster, but politics has always been a painfully slow game (Civil Rights took over a decade of demonstrations for example to fix a single issue). This country has always been a bit slow on the uptake, but at least public awareness is generally good.
Fix both of them. In any order. US has both a corruption problem (although less so than other countries IMO), AND an outside influence problem.
There are 300+ million people in the country and a budget of over $3 Trillion / year. We can afford the resources to simultaneously fix both problems. There's absolutely no reason to fix things one at a time.