Keeping a clean and organized house, with three year old triplets. Sounds like an oxymoron to me, there is no such thing as a clean house with young kids.
Not so, with a little thought it can be done. The first issue is safety, with little darlings running to and fro, their survival is the top concern on your list.
Kid proof the whole house. Safety latches on all cabinet doors and drawers. Move all chemical products to a high self in the garage, basement, or utility room. Preferably somewhere with a lockable door.
With active kids, less is more. Having a bunch of sharp edged furniture stuffed in a room makes it harder to maneuver through the maze. Kids don't walk, they run. With a little less stuff in the house they may avoid a head on collision with that heavy coffee table.
Designate one room as their play space. Complete with toy boxes, storage shelves, and closet. This room should house the majority of their entertainment stuff. One room that if they leave some toys out the clutter will be contained.
This room should have the bare essentials in the way of furniture, they need space for their imaginations to work. Some chairs and a bed sheet will make them a fort that will keep them busy for hours. Craft projects, finger painting, messy projects should be done here too. When they grow older it will leave you with only one room to overhaul to bring the house back to normal.
Avoid food stains and spills, enforce the idea that eating is to be done only in the kitchen right from the start. By the time they're old enough to question the notion it will be habit.
Usually one door to the house enters into a mud space, be it off the kitchen, utility room, or even the front door. Train the little darlings to only use that door when going out to play. If they become accustomed to always going in and out through the mud room the outdoors is more likely to stay outdoors.
Even at a young age kids need to know they have responsibilities. Having them pick up their toys before going outside, or putting dirty clothes in the hamper is not to much to ask of them. Be patient and wait supper until their chore is done, buy being consistent they will soon know that a picked up space comes before eating.
There are many tips to maintaining a clean house with small kids, most of them require a little action on the kids part as well. It's all part of growing up and being responsible adults.