Alphabetize them, check your list of games and keep the better condition copy and keep games you don't have if you are trying to collect a full set. Sell/trade the rest. Bulk sales at a discount to save time, individual sales to maximize profits. If your wife is pushing you to clear the "clutter" then tell her it's going to minimize your profits.
If you end up selling cart only games, I'd be interested in seeing a list to see what you have and may pick some up.