I purchased a computer and some other office supplies in Dec 2019 for contract work that I started in Jan 2020. Can I reports these expenses next year in my taxes or do I have to report it this year?
Yes, you can report the expenses in 2020.
The business start date determines whether operating expenses are deductible in the current tax year or whether the expenses must be capitalized.
These capitalized expenses are considered to be start up costs. You may elect to deduct up to $5,000 in startup costs in 2020.
Expenses beyond that must be amortized over 180 months. You would enter these amounts as an asset and amortize them.
(TurboTax provides this category for you).
What Turbo Tax program will let me file both a salaried job I had in 2019 and also a business I started in 2020?
The program you will need will be based largely on your income sources (other than W-2). You can get started in the Free version, and TurboTax will prompt you to upgrade once you enter information that requires a bigger program. Please click here to get started.