Knowing this will be our only trip to Poland, what places would be on the top of your list that we should see?
I'd go with Warsaw, Kraków and Gdańsk. Those three will give you the best possible tourist experience - Wrocław and Poznań are nice, but they aren't must-see. The only problem is logistics, but - I can suggest something.
Fly into Copenhagen - there are plenty of flights there from the US, and it will be a great starting point. However, unless you have a personal reason for visiting (such as always wanting to see it) - it's not that great, and doesn't contain anything particularly impressive. I'd actually rather suggest visiting Berlin - the history there is much more 'now', and it's a great place to start such a trip.
From Berlin, you can take the Berlin-Gdynia-Express train, which runs straight to Gdańsk. You can then visit the WW2 Museum and the European Solidarity Centre, both of which are must-sees. The Gdańsk Old Town is loved by a huge amount of tourists as well.
From Gdańsk, I'd suggest going to Warsaw, and using it as a base to visit Mosciska. You can also see many important things in Warsaw, such as the Warsaw Uprising museum and the Museum of the Polish Jews. It's then very easy to go to Kraków to see the attractions there.
Then everything is easy - I would suggest the Kraków-Budapest night train (with a private sleeping compartment). You can then go from Budapest to Vienna, Vienna to Prague and then Prague via Dresden back to Berlin for the flight home.
I'd suggest something like this -
Berlin (3 nights) - the city is so full of history that it deserves 3 days.
Gdańsk (2 nights)
Warsaw (3 nights, including trip to Mosciska)
Kraków (2 nights - third night is on the train)
Budapest (2 nights)
Vienna (2 nights) (you could also stay in Bratislava and make a daytrip to Vienna, which is popular)
Prague (2 nights)
Dresden (2 nights)
Berlin (1 night)
All of these cities are well connected by train, and apart from the Kraków-Budapest leg and the Berlin-Gdańsk one, all of the connections are around 2-3 hours.
I can suggest a great agency (run by an American, but based in Poland) that would reserve all the tickets for you, and then send them by courier to the US so that you don't have to worry about anything.
Also, is it feasible to think we can do this on our own?
Absolutely. I'm more than willing to help you put everything together - and for certain you can do it for far less than $6000 for two weeks.