I was reading through here, and not all this information will stand up in case you get audited.
To be on the safe side, take depreciation on anything purchased for your office over $100. You depreciate computers, you write off printers/cameras if they are under $100.
If the computer/printer/camera is used for personal use, then keep a log of the percentage of time spent using the computer/printer/camera for the business.
It's more economical and advantageous now to just claim the standard deduction for office rather than keep track of all the expenses.
Take a picture of the odometer of your car on January 1 of each year so you have a substantiated mileage record since all digital photos carry a date/time for the photo. If you have a big car (and gas hog) it's more advantageous to keep track of expenses. If you have a smaller, gas saving model, it's more advantageous to take standard mileage.
IRS form 2106 is your friend, particularly on line 7 and also for vehicle expense.
The intent of working as a shopper determines if your work is a "business" or a "hobby". You should show a profit to be a business, but if you don't show a profit, you can still claim the independent contractor business status as long as you can show through records that you are changing your business ways to improve the income.
The term "ordinary and necessary" becomes important in expensing items with reimbursement and the more unusual aspects of mystery shopping. Pub 535....
To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary.