How to Sell?
When selling a collection, there's a single fact to keep in mind: every method of selling involves a tradeoff between time spent and money earned. Being extremly patient and selling off piecemeal over a long period of time will maximize the money gained, while selling off quick is quite possible so long as one takes a sufficient hit to the bottom line.
Only you can determine exactly where your own time/money balance is struck. Read on for descriptions of each method, sorted with money maximizing at the top and time minimizing at the bottom.
Imagine paying $1000 for 2000 cards. Now imagine paying $0.50 for a card. If you thought the first was a lot and the second not a big deal, congratulations: you've just discovered why selling retail works. People consider money differently when it's in big chunks vs small chunks, even when it's proportionally the same thing. You will thus invariably get the absolute most dollar-per-card if you sell individually.
You will also spend years doing it. After all, if everyone already has ten copies of Weight of a Legacy, then who on earth are you going to sell your copy to? You're going to need to be patient and wait for the people to come to you (or your listings), and you might not ever move some of the more unexciting stock. Therein lies the rub: a card you don't sell is worth $0.
If you have enough cards to fill out a complete set (or all of the commons/uncommons/rares of a set), then this is perhaps the most balanced sort of listing you can make. People are lazy and want instant gratification, so if you do their work for them they will be willing to spend a bit more for a package deal.
Emphasis on a bit. You will not be able to tally up the cost of each card in your complete set and charge that amount; people expect a discount when moving product in bulk. Not to mention, people who need most but not all of the cards in the set won't like needing to pay too much for cards they already have.
List each complete set you have separately and you will find product moving in a reasonably short amount of time, proportional to how popular/rare the set is.
A "lot" is simply a bunch of something. In this case, your shoebox (or industrial shipping container) full of cards that you're trying to move all at once. This is the Fire Sale of options; people will expect to pay pennies on the dollar, and if you meet their definition of a deal (or a steal), you will be able to move the lot nearly as fast as you can list it.
You will be taking a significant overall hit in dollars-per-card. For 1,000 common cards this may not be worth worrying about, but if you have a good chunk of rarer cards you may find yourself losing out by packaging them together.
Of course, there's no rule that says you have to pick only one method. In general, for people looking to liquidate their entire collection, here's what you do: list the most exciting cards individually (your rare promos, masterworks, rare foils), as many complete sets as possible on their own, and then the rest in one or more lots. If you have a truly mind-boggling number of cards you might manage to pull off multiple lots, but if it's mostly garbage that you never found a use for, don't expect other people to be able to manage any better.