I have ordered a few items from both firstcry and goodlife and have never had an issue so far. I get the delivery in Pune within 72 hours. From my online shopping experiences so far panning a couple of years and near about a 100 orders I can safely conclude that it is preferable to order from websites that have their own delivery service especially when it comes to big cities.
Every single time I have had a problem it has been with websites like homeshop18 that send you junk and then ask you to ship it back to their vendor based out of some cave in Kandahar for exchange. So if you are new to online shopping preferably order from flipkart, myntra, jabong, firstcry, goodlife, babyoye.