Honestly, it all depends on what you are looking for, must have, preferences, etc. You also don't say what % of what type of road you are riding, i.e. 70% paved, 20% gravel roads (rocky???), and 10% dirt. Also, what is the max width tire your frame can accept in the front/back.
That said, if you MUST have great traction off-pavement, then a somewhat aggressive type MTB tire is what you want but know that the paved traction and rolling resistance may suffer.
If you want an all-around tire used by many cyclists doing an epic "round the world" tour which typically encompasses paved to gravel to dirt and some limited rough rock roads, look at
https://www.schwalbetires.com/bike_tires/road_tires/marathon_mondial by Schwalbe Tires. It is a pretty good jack of all trades, master of none tire with good durability and puncture resistance. Be sure to buy from a reputable dealer as there are fakes out there.
I personally would use as wide a tire as your frame fits reasonably if doing much off-pavement roads. With it, you can lower the air pressure and it will ride a lot better and grip better than a typical road tire without flatting near as easily. However, on paved roads, the a wider tire MAY slow you down, especially if not inflated properly.
Hope you have a great ride!