Media Mail is the only way to go as far as I'm concerned. With a good mailer you'll probably have to pay the 2 lb rate for a single album. That's currently $5.22.
One of the nice things about Media Mail is that they don't zone it so entire continental US is same price for same weight. I've also found that they often beat their delivery estimate, but of course you can't count on it.
I use the Mighty Music Mailers from Bagsunlimited because they offer corner protection, but they are pricey. Plenty of options out there though for lesser cash. A lot depends on how costly your albums are. Crying shame to bust up the corner of a $100 record, $5 records a different story as far as how much you can invest in packaging.
I've had good luck on Discogs with the genre of music I have in my collection.
Good luck
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