Transfers of property pursuant to a divorce are not taxable. We can ignore most of your situation, you will end up with a house and some number of shares of stock. It doesn't matter how the number of shares was calculated.
When you sell the stock, you will have capital gains equal to the difference between the selling price and the cost basis. The cost basis is what your husband originally paid for them. If the shares were awarded as part of his compensation or bonus for working, the cost basis of the shares is equal to the value that he paid income tax on.
Shares acquired in different years will have a different basis. If you get the oldest shares, they were probably cheapest when acquired and so will have the largest capital gains when sold. If you get the newest shares, they were probably most expensive when acquired and will have the lowest capital gains when sold. In other words, even though you sell the shares for the same price (today's market price), the amount of taxable capital gains will vary depending on the age of the shares you sell and the price when those shares were acquired. You are going to have to work with the stock broker to manage this situation, and to document the basis of the shares that are transferred into your name. You may also need to discuss with your attorney to have your divorce agreement specify which shares you get. (It might be most equitable to get the shares as they were spread out over time. Suppose he received 500 shares a year over 16 years. It might be fairest if you were to receive 250 shares from the 2001 batch, 250 shares from the 2002 batch, and so on.
Whatever you decide, you need to document your basis in the shares because, if you are audited and can't prove your basis, the IRS can reassess your taxes using the lowest possible basis resulting in the highest possible tax.
As long as you or your spouse held the shares at least one year, the gain will be a long term capital gain and will be taxed as a lower rate than ordinary income, In your situation with $32,000 of other income, the first $22,000 of capital gains will be taxed at zero percent, and any gain over that will be taxed at 15%.
