We have hampers in each bedroom with flip lids. It really depends on how your house is set up. In our new house the laundry is on the main floor instead of the basement. So we have a hamper in each bedroom (6 people, 4 bedrooms) and one in the main bathroom where two of my triplets bathe so they're not walking through the house naked, lol. I also have a hamper in the laundry room where the stand up freezer is so I can easily slide that hamper around in the small area. That hamper is for left over things like a stray towel or shirt. Also, when a hamper is brought in and I load the washer and there is some left in the bedroom hamper, I'll put the excess in the rolling hamper so the bedroom hamper can be immediately brought back to it's own room.
I found a nice hamper at Walmart where the back side is flat to go against the wall and has flip tops to keep toys out and not looking directly at people's dirty clothes, lol.
Your best bet is to set up a laundry schedule. Let your family members know when it's their turn to bring their hampers in so you can basically do one hamper a day. We have a very large capacity washer so one tall hamper can fill the washer. If we don't do at least one load of laundry every day we're swamped. We have a family of 6. We also reuse our own towels as well. My SIL thinks it's gross but I know more people who reuse their own towels than not, especially to cut down on laundry. I can't imagine if each person in our family got a clean towel every day! 6 people, 6 towels a day x 7 days in a week = 42 towels a week! I don't even own that many towels and I'm not racking up my electric bill for all of that. Course, my SIL has no children so that works for her, lol.
About the diapers. If you have to haul away your garbage (kitchen, food, etc) away to the dump, where are you storing your regular garbage? It didn't bother us to pump dirty diapers in the regular trash can in the house. The poopy ones just got double bagged. If you take them outside then get a small garbage can for the outside with a lid and put a bag in it and toss the dirty ones there. Keep a can of bug spray and fragrance spray next to the bin and use as needed. Then tie the bag up when it's time to go to the dump. I have used the Diaper Genie years ago with my now 15 year old, back in '95 - '97, but they weren't as nice then. I assume they're better and I see they are larger. I does hide the smell some but I found it no better than double bagging and putting in the trash in the kitchen.
K. B
mom to 5 including triplets