I own a Pen GTi 320, great little indestructable reel, can store a good amount of line,a nd has a reliable drag system. I pulled up my fair share of halibut on that reel. As for sturgeon, the reel would work just as well. I can't really speak much about a suitable rod, but I know that trophy makes a rod designed for sturgeon, I've only seen it used from boats, but you cast with it, so I'm guessing it wouldn't be too different on shore.
You probably wouldn't want to put your calcutta and a trophy rod of that weight to a sturgeon unless your are extremely confident about your fish-fighting technique. I think I snagged a large sturgeon a few years ago (before I had been converted from bottom bouning snagger), I never saw it, but it slower moved upstream and then back again. I was using a similar set up to the one you described, 20 lb test on a drift rod, broke it off at the mainline.