Having two sharp, solid knives, one small and one big knife, is the most important tool for cooking along with a honing tool to keep the knives in good shape so they last a long time and a cutting board that is toxic free. I have one cutting board to cut meat and another one to cutting board to cut everything else.
Amazon Basics Knife Set
Check out this video and article to learn how to hone a knife correctly.
It is recommended to hone your knife after every time you use it and sharpening is usually only needed once or twice a year.
Check with your local QFC store to see if you can bring your knives in when they have their knife sharpener come in to sharpen their knives. They will usually let you do this for free!
Check out this article on why it is better to not sharpen your own knives.
Other cooking supplies that you will need which you can find at a thrift store or neighbor giveaways, garage sales, etc. are a glass mixing bowl, glass storage containers for leftover food, a mixing spoon, baking sheet and frying pan.
Cast iron is preferred over teflon due to the toxicity with teflon. Non-coated stainless steel and ceramic can also be better than teflon. For more information about the pros and cons of pots and pan cooking materials go here.
There are other cooking equipment that can make cooking a little more enjoyable, but are not necessary, such as a blender, muffin baking tray, cookie baking sheet, and casserole baking dish.
Here are some non-essential cooking products I use:
18 Piece Pyrex Glass Storage Containers - BPA free, Microwave, Oven (not the lids) and Freezer safe
Glass Mixing Bowls
Vitamix blender
Ninja 6 quart slow cooker