To cut down your scraps, you can use any supplies that you already have on hand in your sewing room. An iron, a ruler, a rotary cutter, and a cutting mat are all that you need.
This is a list of the tools that I prefer and the containers that I use for storing cut scraps. You can use whatever works for you, so don't feel like you need to run out and buy new supplies for this project.
My favorite rotary cutter
My favorite rulers for cutting scraps
8.5" square QuiltCut Ruler (I think it only comes as part of this set, but it's a great, non-slip ruler and much more affordable than the Creative Grids)
My favorite cutting mat
Creative Grids 24" x 36" - there are less expensive mats out there, but this one is thick and it has held up very well to the amount of cutting I do (a lot!). I have tried other brands and this one has been the best.
(I know some people like to use a rotating mat when cutting scraps, but I find that all of the scrap link gets in the mat and makes a mess so I don't use one)
My favorite iron
Oliso Smartiron with Auto Lift - I need to do a thorough review on this iron. It is great — the two main benefits are that it gets very hot and I love the auto lift function.
Chi Iron - If you want a very good iron that is about 1/2 the price of the Oliso, I used this for years. The main negative was that I felt like over time, it stopped getting quite as hot.
My favorite storage boxes
Ikea Variera Box - this is a great option if you don't want a lid
Hopefully this gives you some ideas to get started!