I think the baskets are a great idea. I just think you need smaller baskets
I have 3 kids (6, 4, and almost 2) our house is relatively small, we have a living room, kitchen, dining room, and our bedroom on the first floor and 2 bedrooms upstairs (2 boys in one, and girl in the other). The kids aren't allowed to bring toys into the dining room or our bedroom. So I have a small tox box in our living room for the youngest to keep toys downstairs since he's not allowed to go up and down on his own. All the toys that are on the first floor go in that box. If it gets full of toys from the older kids then I pick them out and have them put them away. When toys get brought into the kitchen I throw them back into the living room if they are left unattended. So usually a couple times a day I'm throwing random toys back into the living room. The toys that get left downstairs from upstairs go in a small basket on the stairs. When it's full I bring it up. The basket is probably only the size of a shoe box though. Anything that is too big to go in the box needs to be put away as soon as they are done playing with it.
It sounds like your biggest problem is that there are just too many toys. Maybe you could make a rule that certain toys belong only in their room and aren't allowed to come out. Your 4y/o is definitely big enough to start helping pick up his own toys and bring them back to where they belong. DD has tons of those little pet shop things, and mini my little pony's... she knows that those belong only in her room because there are just too many little pieces and if they come downstairs they will get lost or thrown away. If I have to ask over and over for something to get put back where it goes, then I put it away, right into the trash bucket. I'm sure it sounds harsh, but the older ones have learned real fast that way...lol I feel like if they are just going to leave their things around like trash, well then that's where they'll go. Obviously with a 1 y/o that won't work, and it's more about limiting the amount of toys that are available for them to bring around the house.
We also pick up every night before bedtime, downstairs and up. That helps keep the house tidier. I think having a good night time clean up routine helps, and I know I feel so much better relaxing after the kids are in bed with a picked up house.
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