Get the kids to carry something. It makes them happy and involved and also can actually spread the burden around, especially if they are bit older and can carry their own weight (not literally, that's too much already). Even our three year old went on the plane with a kid-sized backpack stuffed with HER diapers and HER change of clothes and some of HER toys. She felt quite, well, empowered by all this and when we needed a diaper it was handy.
Don't necessarily pack one suitcase or pack per person, because if you lose that then Dad has no clothes while everyone else is fat and happy. Divide things up to spread the weight around and also to minimize the hassle and inconvenience if one suitcase is lost.
As for suitcases and backpacks, some ideas. Buy expensive and high quality as regards sturdiness and don't spend on looks. Traveling really beats up luggage and if your main goal in traveling is to impress bellboys and baggage handlers buy sturdy but plain bags and tip better.
The most important things with luggage are: locks/catches that will hold, hinges that can strain and not break, lighter soft sided if you are mostly packing clothes, heavier hard shell if you have lots of things that can break, like toiletries.
My wife actually asked for some suitcases recently for Christmas. She got some Briggs & Reiley bags that she loves. You can check them out
Lastly, weight and carry-ability. One huge bag seems like a good idea, but after a couple of hotel to airport moves it will be so heavy that you'll hate it. Also, abroad many times car trunks and doorways are narrower than in the U.S., another reason to avoid huge bags.
We like bags with wheels and extendable handles. The wheels usually break and the handle snaps off someday, but until then they are handy, in many ways like kids. They don't stay the way they started forever. Buy a bag with wheels of a size and packed weight that you can still carry if necessary, say if the wheels break or if the pavement is too rough to pull the thing along. Kids can pull a suitcase that is much heavier than one they could carry.
Handles on both the top and side of a suitcase make it easier to handle. The top handle is good for hefting the bag onto the airline check in scale while the side handle will get you through most doors easier.