In my opinion websites are like business cards...if you are in business you have a business card and you have a website. It use to be that if you were in business you had to have a yellow page ad, but that is being replaced by website also. I do not feel that a website will make or break your business by itself but it helps complement and supplement other means of marketing your business.
Things like Facebook and flicker are tools to help market a website. I would not recommend relying on them completely since at any given time they could fall our of favor or be replaced with the next cool thing like google+ for example. You mentioned flicker, have you ever heard of pBase? That is where I have the most photos since I never got around to trying to move them to flicker. If you are going to have an online presence then you want to own and control your own domain since that will become your online brand. All of the social media marketing tools like facebook, twitter, flicker, google+, and blogs should all revolve around the website. Traffic will depend on how well you market your website.
Cost will depend on what you do with your website, how custom it is, how much you program and how much you have a company program for you. My business is not a photo business but when I first started the site it cost twenty something a month but now I pay a few hundred a month because I need a much more serious and reliable website.