I'd drive over to my LCS and buy about six boxes of Card Savers. I don't have anything like enough of them on hand. Once I got back, I'd sit down and put all of the cards into holders before I handled them any further. I would then do what we all do with new cards: look them over, evaluate what they are, and so on.
If the lot plus what I have add up to some form of set (short or with some mix of rare ones) I'd keep it. If not, hopefully, I could finish my T206 HOFers from the pile. That would be nice. I'd probably upgrade a few of my crappy ones too. That also would be nice.
I'd next call Al at LOTG and ask him to pick up the rest and sell them for me. I know Al would do a fantastic job of sorting the cards, getting the valuable ones slabbed, and marketing them with the personal care he always shows consignors. Maybe I would stagger the sales into different tax years to avoid bracket creep but that's a bit too granular of an answer for the call of the question.
In short, keep the ones I need, sell the rest. After all, it's just stuff and I cannot take it with me when I die. Though I definitely want to be buried in a card suit
Hopefully the cigar boxes are nice ones too. If so, I'd keep those for display.