Hello!
The boxed-roadster (boxster) is a pretty small car, you will feel the swaying so much more than a heavy car so don't panic yet. However you will often hear a few saying that the Boxster is better than average in this regard, so perhaps you got lucky there. Cool little car, you'll enjoy your summer mate
Part diagrams of what could possibly be your issue (e.g. anything!). Nothing technical tho
Boxster 986 Complete Suspension Overhaul
Struts gone wrong will make your rear bounce up/down for no important reasons, and the front will dive when braking if the front struts are toast. Springs are cheap so change those with struts normally. Swaying is control-arms and sway bar bushings related I would say but only a good'ol porche mechanic with muscles and a good bar can tell you.
Just for fun.... it cost a good $3,000 to get a full restoration done on the Porsche 986 (suspension & handling). Very fun... as in new car fun