should i put supplies that I bought for a business like yoga mats, puppy cleaning supplies under the category COST OF PURCHASES; MATERIAL & SUPPLIES or SUPPLY EXPENSE?

Put Supplies under Supplies.  Not under Cost of goods sold.   Both Materials and Supplies go under Supplies.  

You don't need to use the Cost of Good Sold (COGS) and/or related accounts (purchases, labor, & materials/supplies) unless you keep and track inventory, including beginning of year and end of year physical inventory counts and valuations using the accrual basis accounting method.   

Do I need to report inventory?   You can opt to use the cash basis of accounting and ignore the beginning and ending year inventory valuations and enter zero for both.  Just be sure not to double up your entries.