Hello and thank you for your question.
Both father and daughter want the opposite thing in this sort of transaction, so the question becomes "best way for which one, the father or daughter?". The daughter would prefer an asset sale so she can turn around and depreciate the assets purchased. The father would prefer a stock sale so he can avoid ordinary income recognition.
If this is an installment sale (stock or asset sales can be done on installment), mind IRC 453(e) here, which could leave dad 'holding the bag' should the daughter sell before paying off dad:
(e) Second dispositions by related persons
(1) In general If-
(A) any person disposes of property to a related person (hereinafter in this subsection
referred to as the "first disposition"), and
(B) before the person making the first disposition receives all payments with respect to such disposition, the related person disposes of the property (hereinafter in this subsection referred to as the "second disposition"),
then, for purposes of this section, the amount realized with respect to such second disposition shall be treated as received at the time of the second disposition by the person making the first disposition.
Should you do an asset sale, consider IRC 1239, which tends to state that the father will be denied capital gains on the sale of depreciable property because he is selling to his daughter.
(a) Treatment of gain as ordinary income In the case of a sale or exchange of property, directly or indirectly, between related persons, any gain recognized to the transferor shall be treated as ordinary income if such property is, in the hands of the transferee, of a character which is subject to the allowance for depreciation provided in section 167.
The tax consequences are not determinable fully from the information provided. Namely, the book value and fair value of assets have little to do with the tax code, save for perhaps determining and allocating the sale price to items in an asset sale, etc. What matters is 'basis' in assets... the father's basis in his stock for a stock sale and the corporation's inside basis in its assets for an asset sale will be used for determining gains and losses. Generally put, amount realized less basis equals gain (loss) (IRC 1001). In addition, a lot of other information would be necessary / useful, such as the ability to review the assets and prior tax returns of all involved including the corporation, any current year tax planning outside of this sale for all parties involved, and retirement/estate/gift considerations, etc. If dad is in a high tax bracket, for example, then perhaps it would be best for the family if the daughter takes on more income from this sale.
I do hope this is helpful. Thank you again for your question!