Chorus is awesome! Thanks to its over use in the 1960's, it's sound can make a whole song sound bluesy. The Walrus Audio Julia is the best chorus that I know of and is also the most vintage sounding, which is essential for a chorus to sound bluesy.
A light overdrive is all you need for jazz :). Not too much drive to kill the genre of the song but just enough for a nice break up when exaggerating a note that augments to your tonne and emotion. An overdrive such as a Ibanez TS-9 which mildly changes the tone of your guitar. This pedal sounds amazing in jazz, depending on what settings you use. You could also get a transparent overdrive (an overdrive that doesn't change the tone of your guitar, but just adds drive to it) like the Emerson Paramount which also sounds very good in jazz. Both pedals also add sparkle to your sound and that is essential in jazz otherwise you can sound a bit dull, which can pull you away from the rest of the band. Both pedals are very well known in both jazz and blues worlds.
For blues you should be looking for pedals with higher gain. So a pedal with a higher gain would be a distortion pedal :D. Similar to an overdrive pedal a distortion pedal will add a lot more drive and a lot of drive in blues sounds amazing. The ProCo Rat is famously used in blues/blues-rock for a reason. It sounds amazing and perfectly fits the guitar tone that defines blues.
An alternate to purchasing a distortion pedal is to stack two overdrives (use two overdrives at once) to achieve the same drive as a distortion pedal but with more clarity and better toning options. Which overall has more versatility. However can be more costly $$$. Here are some good overdrives: JHS Superbolt, JHS Morning Glory, Klon KTR, Selgah's Scarlett Love V3 and the previously mentioned: Ibanez T-S9 & Emerson Paramount
Hope this helps :)