What is the best way to buy a weekend trip to Agra from Mumbai to visit the taj mahal?

Do I have to fly to Delhi and then take a taxi? Which airlines? or should I look for a package?

Let me first clear you that there is no plan to close taj mahal for months !!!!. they are planing to cover taj with Muldani mitti to clean it....But that will actually once in a life time to see taj in a diffrent color.

Well you need one whole day if you want to visit Taj, Agra Red Fort and Sikandra.
If you want to go to fatehpur sikri add one more day.

Agra is well connected with delhi by rail rout and by road.

Shatabdi takes only 2 Hr to reach agra from del.
I will recomond Take flight from Mumbai to delhi take cab from delhi you will be in Agra in approx 4 Hr max.
Dont take any Package just book a taxi and if you want to stay book a hotel there is nothing that will come extar with packege.
Hotels: My recomondations :
5 star : Taj view (you can actualy see taj from ur room window)
4 star : Holiday inn
others: Hotel Kantt

The best way would be to board the August kranti in the evening from Mumbai central / Borivalli and get down at Mathura. From Mathura you can take a cab or a train to Agra.

Its better than flying to Delhi as you save money plus the time is not wasted and you can spend more time in Agra.

Board at Mumbai central at 5:40 get down at Mathura (9:00) nxt day, go upto Agra you will be there latest by 10:30 am enjoy in Agra the you can take the same route and train back. (Board from mathura at 6:40 pm and be at mum at 10:15 am the nxt day.

I would say do it yourself dont go for a package

TAJ-MAHAL IS GOING TO CLOSE FOR VISITOR COUPLE MONTHS FOR SOME REPAIRING, CHECK DATES BEFORE YOU BOOK YOUR TICKETS.

package deal could be expensive in india, you can buy seprate flights, its always go by flight as we are flying from another country, i think you wont prefer indian train, and its very long journey. Could take 1 day ... so flight is best option.

try to look different domestic option, go air, Air deccan, kingfisher.

price always depends on the period you fly, if its not peak season you might get cheaper deal.

look for the better value for the money.