If you have the ability, I highly recommend at least a 4-night. The first day, your room is ready at 1:30, you unpack, start to figure out where things are on the ship, leave port around 4:00pm or thereabouts, see a show and have dinner. Every cruise we have been on, the first night show is an advertisement more or less for what to expect the rest of the cruise.
The 2nd day/night, you'll have completely open. Then the last night always feels rushed to us -- they really push you to complete the survey, get your bags packed and outside of the stateroom by 10:00, etc. And the next morning you are up early and get kicked off the boat before 10am.
As a first time cruiser it might be a little overwhelming, and you might not feel like you got the chance to relax.
Most everyone on here will say longer is better. Our first cruise together was a 4-night, and we agreed it was too short, we cannot imagine a 3-night. It'd be one thing if we lived close and could drive and do it more often, and maybe thats your case. But we have to fly, so flight cost is roughly the same whether its 3-nights or 7-nights. The cruise cost, per night, is typically a little cheaper the longer you go (but not always). We've got to get a hotel the night before whether its a 3-night or a 7-night. So for us, the bang for our buck starts at 5-nights.
I urge you to consider a 4-night. Either way though, enjoy your cruise!