Are you trying to maximize your ROI or simply to de-clutter? If it's the latter, then offering the collection to a local vinyl store is the easiest way to be rid them. If you want to get the most for each album, or at least the ones you think are in demand, then eBay or possibly another forum specializing in LPs, is the way to go. But, shipping something fragile like an LP will be expensive and time consuming and may result in more than a few returns.
If it were me, I'd post something on Craigslist and FB Marketplace and see what kind of offers I received. The listings are free and you may get an idea of the value of your collection. That is where I start all of my selling now. Leakage from eBay and PayPal fees runs ~13%, so I can drop my asking price by 10%-15% and still come out about even if I can sell locally. And no shipping!
Edit to add -- I am selling stuff that is declining in value and that I no longer need, so I'm coming at this from the "every $$ I make is positive and it's out of the house" perspective.