What should my heirs do to dispose of my vinyl and CDs?

For your relatives without experience with vinyl, eBay or Discogs will take too long and be too much of a hassle, especially going through each record one-by-one grading.

Depending on where you live, the easiest/quickest thing for your heirs to do with you LP and CD collection would be for them to call up an area record store or three and ask for an offer on the whole collection (maybe let your heirs know the rough value). Assuming you have a worthwhile # of collectible LPs any record store owner will travel far to make a house call to pick up a valuable collection.  Depending on the number of rare/collectible records, they'll probably only get 25-35 cents on the dollar, but will be quick and easy.

My solution is to divide the systems between my three children. Once they have the components, which will be split so that each child has a nice functioning systems they can either get excited and keep their system or they can sell it on their own and make a little bit of money. I will even out the value the best I can by identifying some of the extra components should go to the children with a lesser value complete system. I am lucky that my children will not bicker over a tiny bit of money difference, so I believe.

One of my children is totally into music so that is an easy decision who gets my main system. They also have the space for a larger system while the others will be very content with the smaller systems, all being nice system capable of producing a great sound. I am going to go over the entire process well ahead of the time they will be split up. Should be an interesting discussion.

Concerning the CDs I still own, my son in-law loves music and is an avid collector so he is the logical choice to hand this collection down to. Any discs he does not want can be sold off and the money split evenly. He buys and sells CDs and Vinyl regularly.

I say melt it all down in the form of a casket, then you really can take it with you!😁

I don't worry about what my family will do with my stuff. My wife and kid hate music (yes, it is true). I will, as time passes, watch for a younger man who has genuine interest in this type of stuff. Yes, they ARE out there. I will make sure he gets it, lock, stock and barrel at zero cost. Same with my prodigious watch collection.  Of course if I get run over by a bus tomorrow, I am sure my 3,000 CD collection will be on the curb before I am even cold. 

Point is, I am indifferent if my family makes any money on my stuff. I am more interested in somebody younger who might not be able to afford what I have and would be pleased to have it and maybe think about me from time to time. 

I imagine guys with big ham radio rigs wonder about these things too.  

In your specific case @timintexas, what a great offering that would be. Wonderful post by the way.