We do know that Jesus was probably in his early 30s when he began his ministry and would not have had long hair.
It's fair to assume that Jesus had a beard, in light of first-century Jewish culture and tradition—though Scripture doesn't say this explicitly. (Isaiah 50:6 says the suffering servant, ultimately exemplified in Jesus, has his beard plucked out, but the NT doesn't cite this).
Isaiah's messianic prophecy suggests that there was nothing unusually attractive about him ("he had no form or majesty that we should look at him, and no beauty that we should desire him," Isa. 53:2)—though it's taking it too far to say that he was thereby unattractive or homely.
He was a Galilean Jew who spent a lot of time outdoors, so his skin tone would likely be a darker olive color, as is typical of those in Mediterranean countries.
In December 2002 Popular Mechanics did a cover story called "The Real Face of Jesus." The positioning of the piece was obviously sensationalistic. But it was nevertheless quite interesting. Using "forensic anthropology" scientists and archaeologists combined to investigate what a first-century Galilean Semite might have looked like, with medical artist Richard Neave commissioned to do the rendering. The article describes the process:
The first step for Neave and his research team was to acquire skulls from near Jerusalem, the region where Jesus lived and preached. Semite skulls of this type had previously been found by Israeli archeology experts, who shared them with Neave.With three well-preserved specimens from the time of Jesus in hand, Neave used computerized tomography to create X-ray "slices" of the skulls, thus revealing minute details about each one's structure. Special computer programs then evaluated reams of information about known measurements of the thickness of soft tissue at key areas on human faces. This made it possible to re-create the muscles and skin overlying a representative Semite skull.
The entire process was accomplished using software that verified the results with anthropological data. From this data, the researchers built a digital 3D reconstruction of the face. Next, they created a cast of the skull. Layers of clay matching the thickness of facial tissues specified by the computer program were then applied, along with simulated skin. The nose, lips and eyelids were then modeled to follow the shape determined by the underlying muscles.
How tall would a first-century Jew be? "From an analysis of skeletal remains, archeologists had firmly established that the average build of a Semite male at the time of Jesus was 5 ft. 1 in., with an average weight of about 110 pounds." I admit that it feels a bit strange to think of being over a foot taller than Jesus! But it's good to have our cultural preconceptions—even prejudices—challenged.
Of course no depiction can tell us what Jesus looked like for sure. But the following rendering is undoubtedly closer to reality than the typical rendering by artists and film-makers: