I'm a "Nashville Guy" and I'd recommend that you use plain gut for the G&D. Gamut is the best but they're pricey. There are many options for the E&A. I wouldn't recommend plain gut on the lower strings unless you're doing all slap or want a total thud on those notes. You can use the traditional roundwound gut or a bunch of other choices. My personal favorite is Pirastro Pizzicato, a semi-flatwound, gut-core string. This set up is great for all types of "roots" music, as well as an older jazz sound.
I'm not sure about "more metallic" (I thought that was the "modern jazz sound"

) or "totally synthetic". The fake guts like Innovation or Supernil give a puffy, somewhat gut-like sound. I always liked the Velvet Animas and Garbos for an in-between string.
Some of these slap/rockabilly guys use solo gauge steel strings
at regular pitch. I think that gives a lot of clickety-click sound at a lower tension.
I have two basses, one has steel (currently Spirocore Weich) and the other has the above-mentioned plain-gut/Pizzicato wrapped-gut combo. They are very different sounds but I like them both. For most of the studio work that I do, it's the gut sound that's needed. Usually it's for bluegrass, blues, retro-Elvis, Patsy, Ray Price, Bob Wills. Gut records well, giving a punchy note that gets heard. Use a dynamic mic (RE-20, 421, M-88) or ribbon mic (RCA 44, 77) rather than a condenser when recording gut bass.
That's my 2¢.