Should I be considering income bracket when establishing how much I owe for taxes when selling stocks?

Yes, your regular tax bracket will affect how much capital gains tax you owe.

It depends on the exact size of your capital gain (rough calculation says about $400k) and the amount of your other income. But the long-term capitals gains tax brackets are 0%, 15%, and 20%. There is also an additional 3.8% Net Investment Income Tax (NIIT) that applies to investment income above $200k ($250k for married filing jointly), so effectively the brackets are 0%, 15%, 18.8%, and 23.8%. You are almost certainly above the 0% bracket due to your regular income. Some of your gain will probably fall into each of the 3 higher brackets. If you keep 20% of the gain for taxes, that should cover your federal liability; 25% if you want to be sure you save more than you need to. However, don't forget state income taxes--most states tax capital gains like regular income.

For 2021, assuming married filing jointly with no dependents and an AGI (before capital gain) of $175k and the standard deduction ($25,100), you have a taxable income of $149,900. This gives a federal tax of $24,475. Adding a $400k long-term capital gain, you add $62,415 of capital gains tax, plus another $12,350 in NIIT, for a total of $99,240 in federal tax. The excess $74,765 from the capital gain comes out to 18.7% of the capital gain.