Was it purely a matter of self-interest, or were there wider economic (or other) reasons that made the United States feel that it had to "make Europe prosperous once more" with the Marshall Plan?
The answers are contained in the Wikipedia paged linked in the question. The quote from US Secretary of State George Marshall's speech at Harvard University on June 5, 1947 explains:
The modern system of the division of labor upon which the exchange of products is based is in danger of breaking down. ... Aside from the demoralizing effect on the world at large and the possibilities of disturbances arising as a result of the desperation of the people concerned, the consequences to the economy of the United States should be apparent to all. It is logical that the United States should do whatever it is able to do to assist in the return of normal economic health to the world, without which there can be no political stability and no assured peace. Our policy is not directed against any country, but against hunger, poverty, desperation and chaos. Any government that is willing to assist in recovery will find full co-operation on the part of the USA. Its purpose should be the revival of a working economy in the world so as to permit the emergence of political and social conditions in which free institutions can exist.
So, apart from the obvious humanitarian goals, the reasons for US economic aid to post-war Europe were essentially both strategic and economic.
Firstly the strategic reasons, in the context of the early stages of the Cold War. The aim was to create stability in Western Europe, while undermining Soviet influence in the East. At the same time, American economic aid would help counter the perceived strength of Moscow-controlled communist parties in France and Italy.
Secondly, the economic reasons. A prosperous Europe would be a growth market for American industries, promoting further growth at home.
You can read much more detail in the record of the debates on the Marshall Plan in the US Congress in the Congressional Record of the 80th Congress (further volumes are also available on archive.org). This includes the observations and opinions of the senate members, which are particularly appropriate in the context of your question.
There is a useful overview of the Congressional Record (and its predecessor publications) which may help you understand the structure of the publication.