First of all, allow me to express my condolences on the passing of your spouse.
The tax filing status after the death of a spouse is fairly straightforward. If your spouse dies during the year, the IRS considers you married for the entire year and you can use the filing status "married filing jointly" when your tax return is prepared.
On the top of form 1040 for your spouse, write "deceased" and your spouse's name and date of death. If there is a personal representative that has been appointed for your deceased spouse, then that person will have to sign the return and if the return is a joint return, you will also sign it. If there is no personal representative then you should sign the return and in the signature area write "filing as surviving spouse".
You may have heard about tax breaks for a “qualifying widow(er)”. If you still have a child that meets certain qualifications, you may be able to file as a qualifying widow(er) two years after your spouse’s death, which will give you the same tax breaks as filing jointly.
If your spouse owned property, the share of that property receives a “stepped-up basis”, which means that when you sell that property, you get a stepped-up basis instead of using the original cost as the cost basis and can use the fair market value at the date of death — this allows you to only owe taxes on the post-death appreciation of the property. This also applies to any assets owned, such as real estate, stock and/or mutual funds. If you and your spouse owned the property as community property, then both halves of the property get the stepped-up basis (not just the half that they owned).
There are special rules that govern if you and your spouse owned rental property. Since it qualifies for a step-up in tax basis to its value at the date of their death, you can use that increased tax basis for depreciation purposes. That means more depreciation currently, which will reduce your taxable income each year until you sell it.
sorry for your loss. since she died in 2019 and you're filing for 2020 your filing status is single unless you were (re)married on 12/31/2020 or you can claim widower filing status (if not remarried) if you paid more than 1/2 the cost of a home lived in for more than 1/2 the year by your:
Qualifying Child or
Parent (you must be able to claim the parent as a dependent by they need not live with you if you paid more than 1/2 the cost of keeping up the parent's main home for the entire year) or
Other Qualifying Relative excluding unrelated individuals and individuals that can be claimed as dependents only because of a multiple support agreement.
for stocks and other items you inherited, their tax basis gets adjusted to the value on the date of her death. sale of any stocks inherited automatically get long-term capital gain/loss treatment.