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It depends. According to this link from IRS.gov., the basis of property inherited from a decedent is generally one of the following: I realize that this publication addresses money but it also means all capital assets used for investment purposes. 

• The fair market value (FMV) of the property on the date of the decedent's death (whether or not the executor of the estate files an estate tax return (Form 706, United States Estate (and Generation-Skipping Transfer) Tax Return)).
• The FMV of the property on the alternate valuation date, but only if the executor of the estate files an estate tax return (Form 706) and elects to use the alternate valuation on that return. See the Instructions for Form 706.

Yes, the long term capital gains on collectibles is 28%. As far as investment expenses, IRS publication 550 defines what investment expenses are deductible. Looking through the publication, I don't see any reference to claiming an expense for the transport of collectibles.  I have looked for other references and cannot find anything that would justify the expense so i will have to say that I would advise against claiming this expense.

I realize this was all overwhelming for you and I wish you luck for a favorable outcome. If you have any additional questions, i am here all day so repost if you need to.