Mt. Rigi on first day from Zurich

Mike, standard statement: Customs takes zero time, just walk through the green "nothing to declare" door. It is de-planeing, getting through the airport and chiefly getting through immigration that will take time. But Zürich has a lot faster immigration than most airports, so 1 hour should be a good average.
BUT, your plane could be late, which could add 1 or 2 hours (or even be early).
BUT, there are two trains every hour, so if you are unlucky you wait 29 minutes (+10 minutes to buy a ticket, you don't understand the system).

GOOD news. Leave your luggage at the left luggage at Luzern station, and go straight to the boat (docks in front of station). saves ½ to 1 hour getting and from your hotel, checking in, up to room, ...).

How often do the boats run in Feb? You need to check the timetable.
And, in Feb you might get a cloudy day when the top of Rigi is zero visibility.
Conclusion: This is total luck, play it by ear on the day.

Hi Chris

Thanks for the tips about leaving the luggage in the station because I thought it only applies for big station like in Zurich
I will be using the Swiss Pass and got it already
So I am not sure if I need to validate it in the ticketing office? Or I can just go to the train station/board the train and validate when the staff checks my ticket?

And you are right, we wi l have to see upon the weather as well!

By any chance, do you where I can find the timetable for the boat because I seem not to find it?

By any chance, do you where I can find the timetable for the boat because I seem not to find it?

http://www.sbb.ch/en/home.html
Put in where you want to go on the lake, and the route planner will show the times. You can also click on the "advanced search" button and then uncheck all modes of transport except "Ship" and it will show only the boat times.

Thanks Sam!
Appreciate that =)

For those who went up to Mt rigi, how long did you stay up there before heading down?
1 hour? 2 hours?
Is there much things to do?
Or just mainly see the views, have a coffee, take photos up the top unlike Mt. Tiltus where theres lots of activities involved?

Mike, The boat times are on the SBB site (all transport in Swizerland is on the SBB site).
You may find the following better: http://www.lakelucerne.ch/en/timetable-fares/timetable/
It lists the boats and their routes, so you don't have to guess the best route.

leaving the luggage in the station because I thought it only applies for big station

Luzern is a big station. There is a whole page about it on the SBB website: http://www.sbb.ch/en/station-services/am-bahnhof/railway-stations/lucerne-station.html

Hello Mike. We were in Luzern in early Sept. and took the boat to Vitznau. The boat was very crowded but the trip was enjoyable. The cogwheel train is a few yards from where you get off. It seems that the trip up to Mt. Rigi took a little longer than 1/2 hour but you can check. Takes time for all those passengers to board and such. Was a great trip up with wonderful views. As I recall we spent about an hour up there taking photos and enjoying the scenery. Many people were having lunch or refreshments. I'm sure you have checked the train and boat schedules for Feb. On the way down, we got off the train at a different stop ( can't remember the name) and walked down to Weggis. The walk down took about 15 or 20 minutes. Weggis is a charming little lakeside village and the boat picked up passengers there every hour (in Sept.). Mark Twain stopped at Weggis in 1878 and started his climb to Mt. Rigi where he spent the night. You can read about this in his book "The Tramp Abroad". The chapter about his journey up the mountain is very entertaining! You might be able to read it online.
As for trying to get to Mt. Rigi on the day you arrive in Luzern, I think, like the other poster said, it would be good to check your luggage at the train station and hop on a boat. The hotels in Luzern are about 15 min. walk from the train station. I hope you have a great trip!