Well, pencil boxes are a great place to start. You can often buy them for about a dollar each. Have your kids make labels for them (colored pencils, markers) etc. and then, find a cupboard or set of drawers for them.
I have one kiddo and different tiers of accessibility for different levels of activity. Markers, crayons, scissors, pencils... in our house we have large cups for these items (as well as rubber bands, hole punch, fasteners) in a basket we call the 'homework' basket. These items are available for use for homework (because we don't need to spend twenty minutes searching down pencils!) and most art.
In a drawer, he must ask for all contents:
In ziplock bags, I have stickers, feathers, art trimmings, temporary tattoos, etc. These must be asked for. I sometimes will grab the stickers on the way out to a restaurant and also grab a set of markers we keep in a pencil box just for outings. (I have multiples, so like the ease of having a set to grab and go waiting in the drawer) We also have some of the messier items in there like watercolor crayons, pastels, glue bottles, glitter glue, watercolors....
And in a bin, I have 'mom supervised' items, including my sets of watercolor pencils and ink pencils, good Micron pens, a variety of better-quality brushes (I still select his brushes based on what he's using/how he is painting. He doesn't understand that the acrylic paints need a different brush than my watercolors, etc.
We also have a basket of paper for him to use. Another cupboard has crafting items (craft sticks, little interesting bits to build/construct with/colored pipe cleaners, etc.), stamps in a box, and I have several available oilcloth pieces, so I will direct him to get one of those before we start. Playdough is stored separately with a basket of various implements.
What works best for me is to have Kiddo ask for certain items and to ensure he gets them cleaned up before we move on. Kids need a lot of help with doing a good cleanup and getting everything to where it should be. I limit access because I want to limit mess. Anything which is self-serve, he could use on a clipboard with paper... very little mess. Messier items which require a prepared area, he has to ask. This cues me to help direct him to prepare his area and cues me to know I need to stick around, just in case.
And I do keep some marker sets separate. Some, I hold back in storage, along with all the extra tape, glue sticks, etc. Kids tend to use the items better when they have less, in my opinion, so we might test the markers every once in a while and replace the colors which are dry, but leave the other stuff in storage. Multiple kids? You might want to let them have their own sets, or make sure there are duplicates of popular colors. Good luck!