Knobby MTB tires suck on the road, wet or dry. The knobs are meant to bite into dirt. When they can't bite, they bend, and that makes handling go straight to shit. Get slicks.
The performance of road tires depends on width and construction. The wider you go, the more cushy the tire will be. 700x32c to 40c is a really good range for all-round usage. Under 30c is the racier end of the spectrum. You can still use those offroad (I've bombed down singletrack on a bike with Veloflex Record 25s) but it can get a little sphincter clenching.
Panaracer Gravelkings are really good for road (wet or dry), and light dirt. They aren't going to be as fast as a good dedicated racing tire (there I'd go for Veloflex anything or Conti GP4K SII, especially now that the latter are on deep discount due to the GP5K coming along), but they're going to be more cushy. The only problem is that they only go up to 28c. Above that, there are the Gravelking SKs, but they are dedicated dirt tires, and the sideknobs make cornering on pavement suck.
For slicks at 32c and above, I like Challenge Strada Bianca, Panaracer Pasela PTs, and Schwalbe Marathon Supremes. The Mara Supremes have better puncture resistance at the cost of a harsher ride and less handling feel. The PTs give up some puncture resistance, particularly on the sidewalls, for better ride and handling. The Strada Biancas go even further in that direction.
One tire to avoid if you're concerned about wet traction is Continental Gatorskins. They're ok-ish puncture-resistant racy tires for dry riding (if you don't mind the compromised ride feel) but in my experience they're dangerously bad in the wet.