Speaking as someone who recently helped a late friend's family dispose of his collection, I will offer the following thoughts.
If it is a substantially large collection (which according to the original post sounds like it is), an inventory will help. However, do not rely upon the inventory and let others to tell you what it is worth. You should maybe look through a price guide once the inventory is made. I am not saying that the prices in the guide reflect what the items in the collection are worth, but the price guide may help you to identify items that are rare and desirable to collectors.
You really have to figure out what you really want, an appraisal of the collection or an offer to buy the collection. What is the purpose of your appraisal? Insurance? or value to the heirs? I would have to say that the value to the heirs could simply be the offers that one receives for the bulk collection.
Dealers who come in are not necessarily going to provide you with an appraisal of the collection, but are rather going to provide you with an offer of what they will pay for the collection.
Any prospective buyer of the entire collection is going to offer about $0.30 on the dollar for the entire collection. The reason for that is that a bulk buyer is going to incur costs relating to selling the collection, including the holding costs (ie the lost income on their funds used to purchase the collection related to the time in which it takes to sell the collection), costs of having tables at train shows, cost of driving to train shows, lodging costs if the shows are substantial distances away, and/or ebay selling fees, and also the risk that prices are going to go down during the time that they own the collection and the time it takes to dispose of it.
There are also issues to consider about the collection itself, such as what condition is the collection in, are there original boxes, and the rarity of the items.
An auction house could be a good way to go, but there are also costs incurred relating to selling the items through an auction, such as the cost of shipping the collection to the auction house and the auctioneer selling fees. Plus one is never guarenteed of the prices that will be obtained in selling a collection through an auction. The other thought on auctions relates back to the condition and rarity of the collection. Although there are likely some rare items in the collection and some premium condition items in the collection, I am guessing the majority of the items are likely to be in average condition and relatively common. If you look at auction catalogs, they are likely to sell rare and premium quality items as individual lots and common and average items as bulk groups.
The last thing to consider when selling through an auction house, is when will it actually be auctioned. In July 2015, I spoke to one prominent toy train auctioneer when helping to dispose of my late friend's collection and he indicated that he was booked solid with stuff to sell for at least 12 to 18 months out (at that point). I mention this for two reasons, it shows the changing demographics of train collection (ie people are dying, downsizing, disposing of their collections more rapidly these days) and it speaks volumes of what train prices are doing for the more common and average condition items (decreasing due to more items becoming available to fewer consumers).
The last thing I can say about disposing of a large collection is pricing. I ended up selling my late friend's collection for his family and there was one goal in mind, disposing of the collection in a timely manner. If you want to dispose of the collection in a timely manner, you are going to have to price the items to move.
There are a lot of trains coming to market and the Lionel price guides that are published on an annual basis do not cover items in the lower quality conditions. These guides are pricing out items that are in good / excellent / new condition. If one prices the lower quality items based on the price guides, they are not going to sell in a timely manner and one will have to discount the items more heavily later on in order to move the items. I know that I refused an offer early on for a boxed modern lionel 700E, because the price guide indicated it should sell for more. Several months later, I sold it to the same dealer who had made the original offer, for much less than the original offer and was glad to finally sell the item.
My philosophy in selling the trains was to get as much as I could for them, but not to refuse a fair offer, even if I thought it might be on the low side, as there was so many items to sell and the goal was to dispose of them.
In the end, I disposed of a relatively large collection of prewar, postwar, and modern trains within an approximate 12 month period. I disposed of the collection through a combination of networking with other train collectors I knew, selling at a local monthly show, and selling at the TCA York show twice (once in the fall and once in the spring). After networking with friends and selling many of the premium items, I held the remaining better items and boxed sets for the TCA York show in the fall and moved a lot of stuff there. My perception was that I attained prices close to or better than auction house prices and my selling costs to the family was minimal (because my friend was such a good friend, I charged only minimal selling costs that equated to any selling costs incurred).
The last thing I will say is that it is very overwhelming to sell a large train collection. Had my late friend not been such a close friend, I would not have done it. There is a lot of work that goes into selling a large collection and I am unlikely to offer to do it again.