I was wondering how much advance one should buy for summers trip to India.
Travel Agent or online will be good option and where to store household stuff as my lease will expire.

Ask your supritendent, they will charge you 100 pm and give you some room to store your luggage. They have enough spaces in building.

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એક જ ટીપામાં હો જાણે સાત સમંદર,
એવા ઝંઝાવાત હજુ હૈયાની અંદર

You can rent from Public Storage or UHaul or many such rentals... based on ur space requirements, u can get it $70+ PM. Plus, u can insure the stuff.