What would be the advantages and disadvantages of selecting people to represent the interests of their states?

Well the advantage: you don't got to go and vote for everything like a Democracy, a disadvantage: you don't know if you can really trust what you representative is doing

The United States has a representative democracy rather than a direct democracy: ... Some critics argue that more people would vote in a direct popular election, ... that are overwhelmingly in support of one candidate might feel like their vote is unimportant ... Pros & Cons of Selecting Government Officials by Direct Election.