Henry has some great suggestions.
There are a couple tricks to getting a satin finish on furniture. The floor variety of poly may be (should be) ok. However, it may be too thick for a good furniture finish. That should be obvious if it is the case.
Realize that with a satin or semi-gloss poly, there is a flatting agent that has to be stirred (gently) to keep it in suspension. If you shake it or stir too vigorously, you will introduce bubbles that would give the "dimples".
Next thing is to get a really nice depth to the finish, you should apply a couple coats of gloss sheen first and then a final coat of the satin. More than one coat of the satin will have a muddy appearance.