For the albums you choose to sell I highly recommend doing so on the Steve Hoffman Music Forum classifieds. If you're not yet a member then join up and start contributing some posts, they don't let you use the classifieds until you become active. I've purchase loads of records, CDs, video and gear there with no problems what so ever as both a buyer and seller.
The key thing as a seller is being accurate in your listing. If you have a records that should command some good money then be sure to play grade them. If you have VG+ or NM record and the sleeve is only G to VG, have a look through Discogs. Sometimes you can fine a cheap replacement sleeve is great condition because the record itself grades poorly and then be able to sell the album for significantly more than you would with the bad covers.
I'm also in my early 60's and facing the same issues of lack of space and play time. Right now I have four cartons of records I need to move on. I'll sell 90% of them on the Hoffman Forum, but it's a fair bit of work and I've been putting it off for a while.
If you have the time, try cataloging what you have on Discogs, it really helps to gauge what you've got and what's really of some value. As that previous poster suggested, donating might be the easiest way to go, so if you've got what you donate properly cataloged then you've got proof of value should the IRS ever question the donation. Just go with the low to middle estimates, the high valuation is generally a fantasy.
Of course you can sell on Discogs, but then you're dealing with them grabbing a chunk of the sales, at the Hoffman Forum there are no fees at all. Although I've made many purchases using Discogs, I've only sold there once, a rare punk 45 single that fetched over $500 within 20 minutes of my listing it. I just had to send the buyer photos to prove I had it on hand and the listing wasn't fraudulent. I was paid quickly and shipped it off to the happy buyer.
Best of luck with everything!

