I have purchased a few collections like yours through the years. I paid about 10-30 cents on average per card.
Believe me, selling cards by singles or in smaller lots on eBay takes years. A few months ago, I came across 3 monster boxes full of signed cards from a spring training in-person collection I bought about 5 or 6 years ago. I literally forgot about those remaining cards. I sold the better ones as singles and am selling them in smaller lots, getting about 30 cents a card as I am down to the commons.
My advice to you, if you have the time and don't want to sell them all as one lot is to pull the better singles. Also, some of the guys you think won't sell individually, will sell. Do a quick eBay search for sold prices to see. Also, you may want to sell cards from certain sets individually, even if they are commons. Sets from the 80s are popular among signed set builders, especially 1987 Topps.
You can also try to sell team lots or, again, if you have the time, sell lots by sets, if you have enough cards from that particular set to do so.
There are a FEW auction houses out there who may be willing to sell your collection. However, be prepared that you may get cents on the dollar per card.
Hope I helped. If you have any further questions, please ask.
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