Hello and welcome.
The first thing you're going to need to get your head around is the different concepts that are out there about exactly what the "value" of a coin is. It all depends on who's asking the question, and why.
First off, you've got the value that the owner of a coin shop is going to give you if you were to just dump the entire collection on their desk and ask them "how much would you give me for this collection, right now". While the crudest definition of a coin's value is "whatever someone is willing to pay for it", this is the quickest and simplest way to convert an estate collection into something more easily divisible and there's some kind of hurry to obtain the funds quickly. However, this "value" is going to be quite low. The dealer, in this circumstance, is not going to look too closely at the collection and will be making lots of worst-case assumptions about the collection, without looking at it too closely. Then, when they have time, they will then go through the collection and pick out the best items from it for individual sale. Coins not deemed worthy of such treatment would be sold in bulk lots. Most dealers will happily give you this kind of valuation for free, even if you make it clear that you're not interested in selling the coins immediately.
Second, there's the "book value". This is the number you would obtain if you were to look the coin up in a coin catalogue or price guide. It would also likely be the price that a dealer would be selling the coin at. This is also the value that an insurance company would want to know for a formal valuation, since that's how much it would cost you to replace it. Coin dealers can do formal valuations, but this takes much longer as they have to spend the time looking at each individual coin and looking it up in the catalogues. You do have to pay the coin dealer an hourly rate for their time if this kind of valuation is being undertaken. Note that a coin dealer will not then accept that valuation as a sale price for the collection. But you can find out the book value of your slabbed coins fairly easily, as the slabbing companies maintain price guides for the coins in their slabs.
Finally, there's the actual value someone will give you for the coins. Unfortunately, this number is unknown and unknowable until someone actually gives you the money. Ideally, you want that number to be as close to that high number from the second definition as possible, but realistically it should be somewhere between those two values. Selling coins on some place like
ebay is an option many choose to try to attain higher prices, but
ebay has it's own risks and issues (shipping and packaging, "difficult" buyers, being mistrusted as a "new seller", etc). I'd only recommend
ebay if you're already an enthusiastic eBayer. For larger collections, especially in the larger cities, dedicated coin auction houses are a good way of getting better value; the drawback there is having to wait until the company is running their next auction. Coin club auctions have also been mentioned by others above as a good option for both selling coins and for learning about coins generally.
My suggestion, given your circumstances: take the collection - in its entirely - to a couple of coin dealers (not jewellers or those "we buy gold" booths, unless there are literally no coin dealers within easy driving distance) and ask them for that definition 1 valuation of the entire collection. They will need to see the actual coins, and not just the list (though the list may be helpful too). Maybe talk through the list of dealers you plan on asking, before you go, so there's transparency with the family there. Get a couple of valuations, and choose the highest. This gives you a number for the estate to consider, as that component of the whole estate. I'm assuming for now that your dad's estate includes other assets other than the coin collection (eg house, car, cash in the bank, etc). This way, the entire estate can be partitioned fairly among the heirs, and you can ask to take all or part of "your share" of the estate as the collection, rather than as cash.
It is "fair" because the valuation you've used is a genuine valuation from a knowledgeable independent third party (not some number you've concocted yourself, or that some random people on the Internet gave you) and you would be essentially gambling that maybe you might get a higher value for some of the items at a later date. Who knows what coin prices are going to do in the future, and you might decide not to sell after all. If, at some point in the future you do happen to sell some or all of the collection and you realise with surprise that someone is prepared to pay you much much more than your estate valuation had allowed for, then you can always voluntarily choose to make a further split of the profits to maintain family harmony - and to remember again your dad who left you that legacy.
I'm sure your dad would have been pleased as punch that at least one of his kids was actually interested in maybe keeping all or part of the collection and becoming a collector themselves. Coin collecting is not a hereditary disease and can be a somewhat lonely hobby, and sadly many coin collectors in your dad's situation find themselves with maybe a dozen or so kids and grandkids, but none of them share their passion or want anything to do with collecting coins.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis
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Posted Yesterday 6:29 pm
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Uncirculated American Silver Eagles 
