Do not go small, as you grow in this hobby, so will the amount of bits and bobs. I got a (https://www.amazon.com/gp/product/B003P0XRH0/ref=ppx_yo_dt_b_asin_title_o07_s00?ie=UTF8&th=1) And It holds all my pins and springs and then some.

I think you might be looking for drawers like these?:Option 1Option 2Option 3Option 4They're all just variations of each other in different sizes & numbers of drawers, all plastic, and around $30 and under. The dimensions are slightly off, but you might be able to find ones that are a little closer is space is a constraint.

If these don't work, you might have luck searching for 'hardware and craft storage drawers', which gave me these on Amazon :)