Over the past year I've tried several ways of keeping them neat and in order and the system I use now is the one I find works best for me. I had to buy a few supplies to help with the organisation but they were so cheap it's possible to utilise this for any budget.
I purchased some small floating shelves from IKEA and store my nail accessories on here.
Bottom box is acrylic system, then stamping tools, nail art pens and cotton balls, then my box of tricks!
To store my nail art brushes, dotting tools and other small accessories like nail stickers and gems I use a shoe box, you can pick up "pretty" shoe boxes from many card shops or supermarkets. I've recently saw them for sale in Card Factory for £2-4 depending on the size. The one I use is from a past Christmas present and I just recovered the too in duck tape (unfortunately you can't get this in England, I got it gifted by a friend in America, on amazon and eBay it's crazy expensive!) In this box I store everything from make up sponges for gradients to brushes, acrylic paints and nail files. I also have a clever way of storing all my gems and bows to save space within the box.
I bought the small zip lock bags off eBay for very little (I also use these for my Scentsy samples I make!) and the bag I received in one of my purchases from an indie maker. I have several bags of studs, gems, bows and charms, which take up a lot less space than their original boxes did.
I hate the cellophane bags in which cotton balls come in, so I use old glossybox and birchbox boxes to store them in. I have around 1000 cotton balls in two glossybox and one birchbox boxes. Again I covered these in duck tape but pretty wrapping paper would work just as well.
I also ran out of space to store my konad polishes and nail art pens on my nail racks, so I am storing them in boxes from nail mail I received.
A box from a Models Own order I received.
A box from a Ciate order I received.
Hope this post has helped give you some ideas for storage solutions! If I had the space and the money I would have Helmers everywhere so I could store everything in them, unfortunately I can't so get creative on storage solutions!