Virginia has neither an inheritance tax nor an estate tax.
Further, since you have owned and used the house as your main home for (at least) two out of the last five years, you will likely not have to pay capital gains tax on the sale (unless the gain, measured by the difference between your selling price and the fair market value on the date of your brother's death) is greater than $250,000.
See https://www.irs.gov/taxtopics/tc701
