I have done: 4 night, 7 night, and then a 3 followed back to back with a 4 night.
My recommendation would be to do a first cruise that is a 4 night instead of the 3 night if it fits your budget and schedule.
Why ?
You get to experience a day at sea.
The trip is longer, allowing you more time to experience the ship, the programming, and to relax.
A PP described well the settling in, relaxing, thinking about packing situation of a 3 night, With a 4 night you get an extra relaxing day in there.
We found the 3 night was go-go-go, even if not by us (we were relaxing since we had a B2B), by everyone else. Trying to get as much into the short time you are on the ship.
Now, we still found downtimes when things or places were less busy -- 'course we were seeking those out, so maybe we found more than most people would. Also, we were familiar with the ship, so we knew things like using the forward elevators to get to our room (which was fwd) instead of the mid elevators -- the fwd are usually less busy and on the first day when they announce you can go to your room, you will appreciate the difference.
That said, if all that fits the budget and time is a 3 night, it will give you a good glimpse into what longer
DCL cruises are like, but it won't give a complete understanding.
3 and 4 night cruises are long enough to give you some experience and help you decide, but not long enough that you feel "trapped" if you decide you don't like cruises/DCL.
When we did our first cruise, a 4 night, we came off knowing we wanted to do longer.
With the 7 night we knew we wanted to do no less than 7 nights in the future.
Our B2B, which gave us 7 nights, we decided we were right about minimum 7 nights, and oh, how about doing even longer, like 2 7 nights B2B ? We may do just that in fall 2017, or we may stay with just one cruise of 7 nights or longer.
SW