Personal recommendations would be:
Toots & The Maytals - my favourite reggae artist / group, very upbeat and a fantastic voice (try the album Funky Kingston)
The Congos - my favourite roots group, try the all time classic Heart Of The Congos.
The Gladiators - great vocal group, Proverbial Reggae being a good starting point.
Bob Andy - great roots artist, another fantastic voice.
The Skatalites - (mostly) Instrumental Ska, one of the most famous groups from Jamaica and with good reason!
Lee Perry / Upsetters - early stuff (60s and early 70s) is mostly instrumental with a fair bit of Hammond organ, try the recently re-issued album Return Of Django, later stuff is just as good but the sound of reggae had changed so for a Dub sound try Super Ape (cannot recommend this album enough) and if you can find it 14 Dub Blackboard Jungle, basically anything Perry had anything to do with turned to gold, possibly the most prolific, influential and underated musician / Producer of the 20th century.
Mad Professor - UK based dub producer, weird and wacky sounds, always good fun, try any of the Dub Me Crazy series.
Would add any 60s Ska will be fairly up-tempo and lively, Rocksteady (also 60s) is slower and more soulful, Roots music tends to be based around Rastafarianism and/or Jamaicans being a displaced people, some brilliant music within this (Congos, Ras Michael, Prince Lincoln), Dub (70s onward) is the forerunner to remixing and is based around the rhythm section with guitars, keyboards and percussion dropped into the mix with extensive use of reverb, echo and delay (King Tubby, Scientist, Lee Perry), Deejay (70s onward) is the forerunner to hip hop / rap and involvers singers 'toasting' their own rhymes over instrumental 'Versions' of tracks (I Roy, Dr Alimantado), Dancehall (80s onwards) is fairly lively but doesn't really do it for me and eventually in the 90s began to turn into what you say you don't want to hear (who does?), good dancehall: Frankie Paul, Barrington Levy.
Won't go into UK reggae here, but from the 90s onwards I tend to move into nearly exclusively UK reggae as Jamaican music moves towards Buju Banton, Beenie Man etc.