Visited a specialised shop, the first card I showed, my Captain America is apparently worth $160 if graded, dealing with bigger issues, just want them gone.
I don't know Sweet F*&k All about the cards you're wanting to get rid of, but I had a modest collection of hockey cards that I just wanted to be rid of last spring.
My collection had a handful of older cards with some moderate value, 4 Oh-Pee-Chee sets from the mid eighties (pre-junk-wax era), a few autographed cards, and the bulk being late eighties/early nineties junk-wax sets and singles. All combined it fit into 3 heavy and bulky totes. I spent multiple hours sorting the cards into their series and cataloging the complete sets.
I looked at online resellers first. There are a couple of them that run ebay auctions on your behalf, but unless your cards are worth a lot, you'll come out the other end with nothing as their fees have a floor, and their auctions are time limited and when the auction ends and you have no bids they keep the card.
To get a better idea about value, I visited a card show. They take place across the GTA pretty much every weekend, and of course you can see what then asking prices are, and most vendors are happy to talk to you about what you have. With the stuff you're talking about, you will probably make out better than me as there is likely more of a market for your stuff.
I found out that the grading thing is a giant scam (my opinion). There's multiple companies, local and international that provide grading services and for the most part the cost of the service exceeds the value of the cards. From what I heard, the local services carry no weight or value in the larger market.
In the end, I listed the small collection of old cards in varying condition as a single lot on Kijiji first. I scanned the cards so it showed the condition well. I got 6 replies in a few hours, with one guy wasting some time but another meeting me here in Port Hope and taking them all at a price I was happy with.
After my investigations and research, I came to the realization that the bulk of my collection was essentially worthless. Sure, some rookie cards from that era (Federov, Sakic etc.) would show up on sites offered for a few dollars but the volume of these things produced back then STILL exceeds demand by a wide margin.
I placed another ad on Kijiji listing everything and offering it for free. I received 4 or 5 responses, attempted to make arrangements with the first guy who responded but he turned out to be a flake. Moved on to the second guy and made arrangements to meet. He was really grateful, was surprised that it was all free, but understood why.
I kept the autographs and the 4 sets that have some value, but I'll list them sooner or later. I'll keep the autographs as most of the guys are dead and some of the cards are personalized.
I got a nice text from the purchaser a day or so later thanking me again. Apparently he was in his basement flipping through the cards re-living his youth.