Plane-train interchange time in Copenhagen

I'm planning to fly into Copenhagen (Kastrup airport) on an early morning flight, taking a train to a business meeting, and fly back in the evening. My schedule will be tight, so I'd like to know what transfer times I can expect between the train and the plane.

I'll assume my plane lands on time (otherwise I at least have an excuse). Approximately how long after the plane arrival time can I expect to be on the platform waiting for the next train (so cross the airport, get from my terminal (2 or 3 depending on the airline) to the station, buy a ticket)? I'll be coming from the Schengen Area, so I won't be going through customs. I won't have any luggage to retrieve.

On the way back, I'll have already checked in online. The airport website has scarily high recommended arrival time, but since it's by company I assume that includes checkin time, not just going through security. How much time should I reasonably allow to get through security in the early evening?