An important thing as a first time cruiser....please do not book it on your own at a website, whether a cruise line site or a travel seller. You need to find a travel agent who specializes in cruises. There are many things to consider and you need a trained agent to guide you. This forum is littered with posts and reviews from disappointed first-time cruisers who decided to 'do it on their own' and they chose the wrong line, the wrong time of year, the wrong cabin, etc.
Please do research on the websites, but when booking time comes use an agent. At least for the first cruise. You'll be glad you did and it doesn't cost you anymore than it would doing it online by yourself.
For perspective - I have been cruising for over 20 years, am editor of this website, have all the press contacts at the cruise lines, yada yada yada, yet I still use a cruise agent to book my cruises. They are an advocate for you.