Hi Praveen –
I have not been in Switzerland in recent weeks, but, unless the weather has been unusually warm, you will generally be at the beginning of Spring in Zürich or Luzern.. At the Jungfraujoch and the high Alpine regions near by, it will be the tail end of Winter. Altitude is everything. So, if you go to high mountains near Luzern – Titlis, Pilatus, you may expect snow and not really “Spring-like” weather a the top.
I agree absolutely with the suggestion to make Luzern your base.
There is frequent fast service from Zürich airport. A train about every 30 minutes. One of them (at xx18) requires that you change in Zürich, the other (at xx47) stops in Zürich but is direct to Luzern. You might make the 1047, but the 0918 is more likely. See the attached screen grab.
On that train, you will come into Zürich main station on track 32, which is on a lowere level. You have 8 minutes to get to track 8 which is plenty for the connection. However, if you miss, catch the next train 1/2 hour later ( or, maybe sooner) .
There are luggage carts available which require a 2CHF coin to loosen them from the queue, and which return the 2CHF when you “plug in ” the cart after you are done at another convenient queue. (The similar carts at the airport are free). The carts go up and down escalators with your luggage on them. Don’t pile it too high, because the carts tip at an angle when they go on the escalator, and bags that are piled high can fall off.
I don’t now tha you will be hiking, but you might take a lake boat on Lake Lucerne. This link will give you some idea of what the lake is like, although you would see more snow:
http://www.myswissalps.com/fo rum/topic/the-swiss-path-and-southern-lake-lucerne
and an attached image or two.
There is a lot of useful information here for your trip. Check the links given on that page:
http://www.myswissalps.com/ab outswitzerland
Slowpoke