If you only have a couple of days, I would just go straight to Luzern and stay there the whole time. You get a bit of everything in one destination - easy transport from the airport, historic old town, beautiful scenery, access to mountains.
Local transportation will be covered by a visitor card from your hotel and this also gives some discounts on nearby attractions. Whether you get a rail pass or not depends on how much you want to do. You really have to take the per day cost of the pass and weigh it against your planned itinerary. If you only want to do one day trip (Mt Rigi plus lake cruise day ticket for example), then you probably don't need the Swiss Travel Pass. If you want to do longer journeys to Berner Oberland or visit a few museums, then you might benefit from the pass (but this will also be more exhausting and less relaxing!). Another option would be to book Saver Day Passes - these are special discounted tickets where you get unlimited travel for a day, 52 francs each. You can buy them online from 6 months out and availability is limited. These are a great option if you don't plan to maximize the benefits of a pass, but would still like the benefits of unlimited travel on certain days. However, just keep in mind that you have to buy them early and can only refund them under limited circumstances.
Fyi, due to track works, there are no direct airport trains to/from Luzern next year, so you will have to change trains in Zurich main station, but this is not too big a hassle. Depending on what time your flight leaves for Egypt, you may be able to take an early morning train from Luzern to the airport. The earliest connection would get you to Zurich airport at about 6:12am. If you have a very early flight, then go to Zurich on Tuesday night and stay at an airport hotel.
