With a limited budget and modest expectations as already established by your selection of speakers (I'm not suggesting that your Polks are a poor choice, Polk actually puts out some good speakers at a reasonable price) it would appear to me that you are locked into an integrated amp or a receiver. The big difference with a receiver and an integrated amp is the inclusion of a phono stage and an AM/FM tuner in most receivers. Additionally most receivers will also include tone controls, which if properly implemented and used, can compensate for some room problems (often no more than those caused by speaker placement often too close to a wall behind them), or source, or component matching issues. Line stages are very popular now but they can be rather limited in the functions they include, and usually cost more, but will probably offer you better sonic possibilities if you don't need the stuff I mentioned that a receiver can.
Now, for someone to comment further on integrated amps which you might be able to use, you will have to furnish some information about the speakers. Polk has many models and I'm sure that their nominal impedence and efficiency will differ substantially. You should supply the model number and these spec's.
It might also be helpful if posters were to know what your long range goals are, assuming you have them at all. Lots of folks are quite satisfied with modest systems and would rather spend their time and money on software once they have reached a certain level (and some want SOTA systems so long as they are on the cheap, so to speak:-). Unfortunately they don't!) Think about it, you could save a lot of time and money over the long haul by being realistic about what you really want or need, and how much money you can really chase after it.
