First the easy part - for 2010 the mileage rate is 50 cents.
With regard to your stock sale - the sale you describe is an installment sale. You need to figure your total gain and then pay tax on a percentage of each principal payment you receive including the down payment. The sales price is $100,000. You will need to determine your tax basis. This is the amount you originally invested PLUS any income earned by the S corp during your ownership MINUS any distributions that you took. There are some other items that factor into the basis, but those are the primary ones.
With regard to your new business - you will end up owing both income tax and self employment tax. For the first quarter, your net income from this business is going to be relatively small. In fact, you could probably say that the NET for the first quarter is $0 due to vehicle expenses and your other expenses.
So, for the first quarter, you really only need to pay an estimated payment based on the stock sale. Whatever your gain is times 15% should be sufficient. For example, if the entire amount is gain, you would pay tax on the $20K you received at 15% = $3,000.
It will be better for you to make some quarterly payments so that you are not subjected to penalties for not paying them when you file your return next year.
For purposes of filing the first quarter estimate, I would probably use the expenses. This is not something that is sent in - it is just how you determine how much to send in. You can decide at the end of the year which way you want to go for the actual tax return filing.