Welcome to the SteyrClub!
Clean it well, if you feel capable, that should include stripping the striker out of the striker channel. If it doesn't already have it, I strongly recommend you buy the Big Taco Delrin cup for the striker guide rod, and if the budget allows, a BT recoil guide rod to replace the plastic one.
For cleaning, I recommend using mineral spirits. Put the slide and parts in a clean baking pan with the MS and let them soak for 30 min. When you clean the striker channel, use a paper coffee filter twisted up tight. Don't use a Qtip, they leave cotton fuzz and often cause problems. I use a dry moly, but any good quality lube will do. Don't over lube the striker - it can cause a failure to fire and we don't want that. On the slide, you want something with viscosity like STP. I use Brian Enos' SlideGlide and love it.
Other than that, just shoot it. If you have problems, let us know, one or another of us can probably help.