Welcome Logger!
I see you are from Washington state. It does matter where your dad had his permanent address ( where he would have been liable for state income tax if applied) when he passed. If it was Washington state, which is one of 7 states with estate tax not linked to the federal estate tax then :
First you should value all assets transferred, including houses, cars, coins, etc. The executor of the will has to do this by appraisals or sales and submit the total value to the court. This will determine the estate tax responsibility. According to the tax rates on the internet if he died in 2008, and had 999,999 or less value, there should be no estate taxes. Neither state nor Federal. Over 1,000,000 it is 14% up for Washington state share. Federal limit for 2008 was 2,000,000. So you might owe Washington tax, and not Federal. If he died in 2009, State tax is the same but Fed is up to 3,500,000.
If it looks like you have to pay taxes ( due to court record of value),
I recommend also to retain an estate lawyer and get an tax accountant to do your forms. The executor will have to do your dad's tax forms until the estate is settled. The one I did for the family lasted 3 years, and no estate taxes were needed.
Now as to Capital gains, the value of the coins you inherit will have an initial basis of the value determined as of your dad's death. You should ( or have the appraiser) if you need one, research what each coin was worth if sold that day. Then when you sell that coin, you are responsible for capital gain ( short or long term) based on any increase in value from that figure, not from what your dad paid for it. If he was alive and gave it to you, you would have to pay based on increased from when he obtained it, but the law assumes that estate taxes would accommodate that.
I am not a lawyer, but have been executor for several family members and started with a "Probate Law for Dummies" and ended up in the county Law library. If a Trust of any kind is involved, ignore above and get an Estate lawyer to make sure the Trust and Trustee is fair and accurate in actions. Sorry for your loss
Jim
