For selling, the basis is the hardest thing for people to keep track of over the years since the Tax Cuts and Jobs Act: A comparison for large businesses and international taxpayers.
The IRS puts this in the employee's hands - to track their own basis. I want to urge you to create a financial notebook that is kept separate from your tax return. Keep it safe and each year, add your year-end statements from all your financial accounts plus a copy of your W2’s. This will protect you down the road as proof of your basis in your various investments. As you go through life, rollovers, RSU basis and sales, and more will be captured for you.
What the IRS sees is cost basis and sale price. When you look at your final forms, the amount listed in cost basis must be the adjusted basis with the wages added. The 1099-B is often wrong.
For receiving, deciding if you should take the section 83(b) Election is key. You would make this election if you think the stock value will go up between the grant date and the vest date. You would also need to have enough cash available to pay the taxes due on the award.
You would not make the election if you think the stock value will go down (or stay relatively flat) between the grant date and the vest date, or if you don't have the cash on hand to pay the taxes.