The first King Crimson album is an absolute classic and should be owned by everyone.
ELP are actually rather good in small doses. I find there's a sense of fun and ridiculousness to their music. Get the first self-titled album and I'd also suggest their take on Mussorgsky's Pictures At An Exhibiton. Also find some live footage if you can, some of it is so OTT it's hilarious.
Jethro Tull though are the gods. I wouldn't argue all of their stuff comes under the term 'prog', but they were definitely one of the more progressive bands of the 70s.
I'd start with the following JT albums: Stand Up [quite blues influenced, a bit of a Zep vibe to it] and obviously Aqualung as it's their touchstone. Also get Living In The Past [a compilation of their early singles] as it's very melodic/catchy stuff.
I'd also say get their late 70s albums - the band moved to the countryside in the late 70s and made a couple of rural themed records. Songs From The Wood and Heavy Horses are utterly essential albums with a very interesting vibe to them. SFTW deals with the mystic feel of woodland myth and lore, there is something very charming about it, very melodic. HH focuses more on the reality of country life, the changing seasons, the old ways of life contrasting with the new, sometimes there is quite a melancholy feel to it.
So get the following Tull albums to start with: Stand Up, Aqualung, Living In The Past, Songs From The Wood, Heavy Horses. Also the 1978 live double album Bursting Out, as the songs are a lot heavier and rawer live.
Once you've got those then feel free to explore the rest of their 70s work. They were an incredibly prolific band. Thick As A Brick is a one-song record but it's very accessible at the same time, so try and get a hold of that. Also Stormwatch, their last 70s album, quite dark and pessimistic.
But really all their 70s work is worth getting. Their 80s work is patchy - Broadsword and the Beast is a great record but Under Wraps is a dated synth-rock anomaly in their catalogue [still some good moments though]. Their 90s work is more organic, Catfish Rising is a good album.
Oh, and if Hawkwind qualify as prog, then Space Ritual is a must buy, preferably on vinyl.
Genesis I find very hard to get into though not bad, and Yes are not my thing at all, the vocals are so flowery and irritating.
Saucerful.... is OK, some great songs there. Meddle, DSOTM, WYWH, and Animals for the win though. DSOTM sounds much better live than in the studio however.
Also get the Live at Pompeii DVD.
I do like Wish and dark Side. I'm not a big Floyd expert as I always associated them with old anorak wearing guys and they do go on a bit but on occasion I like to chuck them on for a bit of a chill out.