The giver is the one responsible for the gift tax, not the recipient. The area of estate and gift taxes is extremely complex and mistakes can be quite costly. It is always advisable to seek the advice of a professional before you make any large gift. You can sell a stock for many times over its purchase price without having to pay any income taxes. It's pulling money out of an IRA that triggers a taxable event.
Any money withdrawn is taxed as ordinary income, even if the money was a result of a capital gain.
Many financial advisers recommend holding individual stocks outside of retirement plans in order to receive favorable tax treatment. If the stock you sold was not held in an IRA, you could have used the more favorable capital gains tax rates. I would like to convert some of my IRA to a Roth IRA this year, but won't know what my income will be until January or February of the following year when I receive my 1099s. Any funds converted will have to be withdrawn and the money will be hit with taxes and potential penalties. Congress is expected to complete a corrections bill to deal with this issue, but they've yet to get anything signed into law.