A look at the good, bad and ugly. First a tip. Make sure you are a PCGS member. PCGS sends emails about upcoming auctions with a list of coins that you need for your registry sets - either a hole in the set or one that upgrades something you already have. Very helpful.
GreatCollections ("GC"). My personal favorite. A modern, easy to navigate web site. A 10% buyers fee, 5% sellers fee (no fees for sellers on coins over $1,000). Great photos. Coins priced for everyone. They have a lot more of the under $100 "every-man" coins than Heritage, Stack's, etc. but I recently tracked two coins that sold for $60,000 each. If you are the kind of bidder who acquires $10k plus coins you would save a fortune in auction fees on this site ($1k on a $10k coin versus Heritage). They ship the day after you pay. They are an internet only auction site - no live auctions. They have one auction a week ending Sunday evening. Coins are usually posted 10-12 days before the auction ends.
Heritage Auctions ("HA"). Most collectors have a love/hate relationship with Heritage Auctions. They are the 900 pound gorilla and sell many of the multi-million dollar collections. Some hates. To search their site for a specific coin is tedious as the site has everything from baseball cards to fine wine. I think they presume you are perusing the big catalogs they mail you and searching by lot numbers. They have a mix of internet and live auctions so you have to stay on top of when your auction closes. Like GreatCollections they do notify you if you are outbid. Unfortunately their big auctions are live and usually in the middle of a work day so responding to a last minute bid shark is difficult. Buyers fees are 20% and sellers fees 15%. They want you to submit at least $5,000 worth of coins if you are a seller. Photos (at least for Lincolns) are terrible. I would not have bought the last two Lincolns I purchased at auction if PCGS images had not been available - the coins photographed that bad. My biggest complaint with HA though is post sale. It takes 2-3 days to get an invoice. It takes a week or two after you pay before they ship. Count on a minimum of two weeks from auctions close to receive your coins.
Things to love. If you buy a coin on their site and have opted to do so in user settings they will contact you if someone has a firm offer for your specific coin in the future. If you buy a coin they will give you a coupon to sell it again on their site with no sellers fees. Like GC you can create a want list. If a 1943 MS68 Lincoln comes up for auction you will get an email.
Stack's Bowers ("SB"). The Tiffany's of coin auctions. Their auctions are smaller and more infrequent than GC or HA but the average coin sells for much more. They sell more of the multi-million dollar coins than all the other auction houses combined (they handled the $100 million plus Pogue sale). Auctions tend to focus on a theme (e.g. Civil War tokens) or a single collection. In March 2018 they had a collection of early Lincolns from the ESM Collection. I would have bought 20 if I could have afforded it. Beautiful, hard to find early dates. They may not have another Lincoln I am interested in for six months. I rely on the PCGS emails mentioned above to let me know if they have something coming up of interest. One gripe, their site doesn't allow you to enter bidding notes as HA and GC do. Their buyers fees are 20% like HA. I believe their sellers fees are generally negotiated since they handle such top dollar coins. They have a cool store in NYC I hope to visit one day.
David Lawrence ("DL"). They have weekly online auctions. They don't have a great many coins at each one. I collect MS66 CAC Texas Commemoratives and for some reason they seem to have one or two at each auction which is saying a lot for such a thinly traded series. They don't charge a buyers fee. They ship timely and no complaints. They don't have a lot of Lincolns but may be deeper in other series I don't collect. I rely on the PCGS emails to let me know when they have something of interest. If you see a coin for immediate sale on their site check Amazon, it will likely be there too albeit at a slightly higher price. People give me a lot of Amazon gift certificates so occasionally I buy from DL through the Amazon site.
Honorable Mention. I've bid on coins at Legend but never won. They sell almost exclusively PCGS CAC. They recently had the only known MS68+ Lincoln Wheat. I could only look at from afar. If you have the money I'm sure there they will have a coin for you. Not an auction house but if you are a Lincoln collector Angel Dee's can have some nice coins. I bought a beautiful Lincoln from their site and it received a CAC sticker soon thereafter.