it's been confirmed that new horizons will have amiibo support, though we don't know what they'll do yet. I'd say you should hold onto your cards until there is more information, not just because you might possibly regret it if they do something worthwhile, but also because you'll have a much easier time selling them when a new game has rekindled people's interest in them.
I've done a lot of trading and selling online, mostly just through tumblr with people who trust me enough to pay me in an informal way through paypal. I've also bought a bunch through ebay, which I'd say is probably your best option if you want to sell a lot of them.
as for mailing cards, by far the cheapest and fastest way to mail them is to get some card stock or a cheap greeting card to put the card in to keep it safe, then mail it in a regular envelope with a stamp. if someone buys a lot of cards you'll need something bigger obviously, but for ~1-6 cards, this is your best option.
Visit my dream towns!
Angie from Maplerow, Ranae from Wayfield and Olive from Yorkwood
I love the cards and I plan to keep mine forever, even if I never use them again. I spent a lot of time and money collecting them all. If they can be used in New Horizons, the prices will probably skyrocket. I think eBay is the best place to sell.