Most value and least painful are two competing goals.
Pick out the most expensive or in demand records, purchase a 20 pack of record mailers, and try to sell them on eBay or discogs to get a feel for how much fun or a pain the process is. If you have no history and thus no seller feedback/rating, it might be difficult at first. Keep in mind after listing fees and paypal fees you're going to take about a 16-20% hit on the final transaction proceeds.
If you're actively a CD buyer, your best value might be to get trade in (store credit) from your local record store. If they don't have your desired CD in stock, I'm sure they'd be happy to special order for you. Best to bring in a couple dozen at a time, rather than your whole collection, since you're likely to get a better deal that way.