You are probably a small business since you do this for profit.
You don't need a tax number (you can use your SSN) but many people like to get a tax number to keep their business and personal separate. You can get an EIN from the IRS online in about 15 minutes.
https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...
Your inventory cost is zero since these are found items. You are responsible for keeping accurate records of your income and expenses even if you don't get tax paperwork or some people pay you in cash.
You file a schedule C attached to your regular tax return that reports your income and expenses and calculates your net taxable income (profit). You pay self-employment tax and income tax on the net profit. The net income from the business flows to your main form 1040 and is combined with your other income, personal deductions and tax credits to calculate your overall income tax.
