The Red Clay Strays, Guy Clark, Beth Hart, Brent Cobb, Old Crow Medicine Show, Lucinda Williams, Tyler Childers, Billy Strings, Dave Rawlings, Doc Watson, The Avett Brothers, to name a few.
I've been listening to a lot of Alice In Chains recently, my all time favorite band. Album doesnt matter, anything they did when Layne Staley was alive. I still like their new stuff too but for me old school Alice In Chains is top shelf. Dirt is a masterpiece and so is Jar Of Flies, Facelift is great too. As for a hidden gem check out an album called Above by Mad Season. Mad Season was a side project, it's Layne from Alice In Chains, Mike McCready from Pearl Jam and a couple other guys.
I know that's probably not considered "classic" but they just don't make em like that anymore. I like a lot of different music but that's the main one right now.