Here's what we did - 5 years later and still going strong! https://www.frugalfamilytimes.com/2013/11/an-organized-playroom-interactive-lego.html
When my son was little, we used plastic totes to store them.
Purchase plastic bins with lids for storage to keep all the pieces together. Get them at your Dollar store.
Get a piece of plywood cut to your desired size. Paint to make it pretty. Have the kids build on the plywood board so the masterpiece can easily be moved.
I got a book case and the ones they wanted to leave together they would store on the shelves for safe keeping. I kept all the other Legos in a Rubbermaid bin and keep the instructions for all the things they could build in a gallon baggie that stayed in the Lego bin or the bookshelf. Whatever they were working on stayed on the cover for the Lego bin until it was finished.