For ska, try-
Madness - One Step Beyond, Divine Madness(a good compilation if you are looking to buy)
The Specials - Specials, More Specials
The Beat - I Just Can't Stop It
Then there's Streetlight Manifesto & Catch 22, who are kinda ok...but i find most ska after the 80s to be quite boring.
Jazz, well, do you want Jazz-rock or traditional Jazz?
If you are looking to get into traditional Jazz, then imo, don't start with jazz-fusion. I find them to be quite different, even though there are obvious similarities.
Kind of Blue by Miles Davis imo is quite a good place to start. Doesn't matter how famous it is. Starting rite from song 1, it's a pleasure to listen to that album.
Other than that, try Song for My Father by Horace Silver and Blues & Roots by Charles Mingus.(a bit more easy going than his other albums)