As an Indian citizen travelling to Portugal, should I book my plane tickets or apply for my Schengen visa first?

There is no exact requirements when applying for a Schengen visa about the accommodation. It is preferred to show a hotel booking, like on booking.com, or if you're staying with a friend, you would need the friend to send an official invitation letter to the embassy saying that he will be responsible for you, but these are only to increase your chances of getting a positive decision. If for instance because of the nature of your trip you cannot provide these exact details, like in my case I was going to do an interrail (I was living outside Europe back then), hence I didn't know where exactly I was going to be after the first couple of days of the trip, I was asked to write a couple of paragraphs describing my most likely route with how I'm going to arrange transportation and accommodation accordingly, and I didn't really have any difficulties getting the visa I asked for.

My advice, be honest and give them openly all the information you have on your journey, they will be on your side.

As for your second question, there are visas up to several years, the longest was a 3-year visa that I've seen so far, allowing you to spend 90 days per year within the Schengen zone. If you're looking for a couple of weeks or months, I'd say as long as it's less than 3 months, the length of the time you're applying for won't cause you any trouble.