The Specials first album should be in every collection. Amazing writing, playing and production.
There is also a wonderful compilation from the 1980s called the "2 Tone Story" that assembled all the English bands together, including the Bodysnatchers, The Beat. Madness, Rico, the Selecter and the Specials.
Island Records came out with a similar compilation called "Island 40th 1972 - 1995 Reggae Roots" that has many of the seminal artists listed above.
I highly recommend "Arkology Volumes 1 to 3" for dub reggae by Lee "Scratch" Perry and some of the newer Trojan Records compilations for lessor known Reggae groups.
A great source of information is Wax Poetics Magazine, which has featured Jamaican artists over their 37 editions. Check out their website.