Do "capital gains" add to your total income for the purpose of determining your tax bracket or are they taxed at the rate of your income-only tax bracket?
No, capital gains are not counted towards ordinary income for determining your tax bracket.
Here is wiki:
Under the United States Internal Revenue Code, the type of income is defined by its character. Ordinary income is usually characterized as income other than capital gain. Ordinary income can consist of income from wages, salaries, tips, commissions, bonuses, and other types of compensation from employment, interest, dividends, or net income from a sole proprietorship, partnership or LLC. Rents and royalties, after certain deductions, depreciation or depletion allowances, and gambling winnings are also treated as ordinary income. A "short term capital gain", or gain on the sale of an asset held for less than one year of the capital gains holding period, is taxed as ordinary income.