I agree 3000 is a bit high. When renting we paid 2000 for 4.5 rooms plus locked garage, including nebenkosts (heat, hot water, cable, garbage, etc., not including telephone and electricity). We're just outside of Luzern (10 minutes by bus or train).

A car is not necessary, and if you want to live directly in Luzern city I would look into www.mobility.ch for the rare occasions you need a vehicle. Luzern itself sometimes resembles a parking lot, and the newest construction isn't helping. You can get a yearly transportation pass which will take care of all your local transportation needs.

Luzern is smaller than Zurich and doesn't have the English-speaking population of Zug, but there are still plenty of people in the shops who do speak English.