This is a bit of an inflammatory question, but it's not against the rules.
However, I'm just going to leave a warning here that top-level replies should be informative, comprehensive answers from experts and not speculation. This thread will be watched closely and bans will be handed out liberally for breaking the rules, as they so often are.
Well, if you were interested in depicting Muhammad visually, the evidence you would need would be at least in three categories:
1: Genetic/Biological - You'd need to know a reasonable way to depict him physically, using traits common to the people born in the Hejaz.
2: Vestimentary - You'd need to know the type of clothing worn in the region where he lived and at the time that he lived. There are a lot of places for this information, but one of my favorites is Arab Dress: From the Dawn of Islam until Modern Times - A Short History by Yedida Kalfon Stillman. There are also tons of archaeological fragments and such that we have collected over textiles, sewing trends, colors, etc. That book above is a fairly comprehensive book on the subject, and Stillman also wrote in a lot of other places about Islamic clothing throughout history.
There are also a number of relics purported to have belonged to Muhammad. Most of these are inside Topkapi in Istanbul.
3: Textual/Artistic - Clothing and textiles were a very big deal during the time that Muhammad was alive, and continue to be a big deal until very recently. That being said, a lot of stuff in al-Qur'an and the Hadith references clothing. The act of giving robes to another was eventually even turned into a ritualized form of honor (See the act of giving the khilat to visiting dignitaries or honored quests during the primacy of the Caliphate. There are even whole books written specifically on this practice.). So, we can confirm certain things about dress simply off of the written evidence that remains. On a less "religious text" note: There are also tax records and trousseau lists that outline clothes as a portion of the inventories of various Caliphs and households throughout the Muslim world. Since clothing was such a big industry, it was a mark of wealth to have a large and varied wardrobe to choose from.
And even though pictures of Muhammad are taboo nowadays: They have not always been so. And even if there exists only few pictures of Muhammad today that have survived, there are lot of images from contemporaries, in addition to statues, coins, frescoes, etc. This ties really well into the second category above.
So... All things considered, your final representation would need to be a swarthy Meccan Arab, wearing a turban, bearded, with likely earthen-toned clothing that consisted of an unfitted wrapped garment or simple tunic, perhaps with a burda or mantle, and sandals. Pretty much the stereotypical image of a desert Arab actually. Muhammad was written to have disliked ostentatious dress, whether that's true or not is better left to others. However, simple block print of animal/figural or geometric designs on fabrics was fairly common, as was striped garments.
Now, there could be some form of conference with the texts for specific scenarios where the description is more clear. For instance, Muhammad on pilgrimage would be unscented, clean, with untrimmed beard and nails, wearing a white wrap or 'izar around his body, with open-back sandals and no turban. Wartime Muhammad would probably wear his usual attire, with chain maille and perhaps lamellar over it, with a helmet. His helmet would likely be wrapped in a turban or other cloth to keep the sunlight from roasting his head. The helmet would likely be of multi-piece construction in 3 or 4 parts.
A note to the Turbans: At the time he was alive, the turban had not become synonymous as a badge of Islam yet. So, not every man would have one, or, if he did have one, it was not guaranteed to be the complex styles you may see today. Simple "sweatband" styles would be just as popular. In all reality, a turban of light, breathable fabric is just a smart idea when you live in a sun-baked environment, which is why turbans are fairly ubiquitous across multiple cultures and times. The turbans themselves would likely have been loosely wrapped. The flat "tulip" style was a Persian thing, and the alternating forehead styles were more Indian, as were the styles with the flanged flap sticking out the top. Most of the turban would probably have the ends of the cloth running behind the head, to the point where the ends could be used to cover the neck. These trails, called rafraf, would later become decorated on future Caliphs.
An interesting side note is that so much of this stuff is known. The textile industry in the Muslim world is easily one of their first truly successful industries. Many places throughout the Middle East are known for their textiles, from the patterns of cloth itself to the ornate rugs they produce. During the bulk of the Middle Ages, there also existed an industry that produced fabric in "factories" known as tiraz, which was embroidered fabric that usually contained Qur'anic verses. In several illuminated manuscripts of the time, like the Kitab al-Diryaq or Varqa wa Gulshah you can see little patches on the turban cloth or sleeves or hems of garments filled with said embroidery.
Anyways, hope this answers your question!
^Edits ^made ^due ^to ^grammar ^issues.
**Visual depictions of Muhammad do not strictly violate muslim law. Infact in Iran today, it is very easy to find images of Muhammad in public market places and households. **
But while the Qur’an doesn’t strictly forbid it, creating an image of the prophet is arguably condemned in various iterations of the hadith — i.e., collections of the teachings, actions, and sayings of Muhammad that many Muslims use an interpretive guide for Islamic life. Many modern Sunni Muslims, who represent the largest single branch of Islam, are sympathetic to this belief. Shia Muslims, however, are far less troubled by religious images, if at all. Depictions of Muhammad can be found throughout the marketplaces of Iran, for instance, which is a majority-Shia country. In 2010, Omid Safi, the Iranian-American Professor of Asian and Middle Eastern Studies at Duke University, penned an op-ed entitled “Why Islam does (not) ban images of the Prophet” in which he described his personal attachment to a picture of Muhammad, which he describes as a kind of family heirloom: http://thinkprogress.org/world/2015/01/07/3609072/what-muslims-really-believe-about-cartoons-of-muhammad/
Some of the earliest surviving depictions are in Persian Miniatures