There's been a whole body of "Quest for the Historical Muhammad" scholarship since the 1970's. There are some great posts in this thread that address the historiography. The biographies and Hadith collections (anthologies of the acts and sayings of Muhammad) are collected and published about 150 yrs after he lived, so scholars treat them with skepticism.

That having been said, we can at least say "Those somewhat later Muslim writers asserted that Muhammad was like..." And according to those writers he was not wealthy. He made a good living as a caravan trader before his calling, but after he started preaching, he his tribe and his followers were put on essentially an embargo. After the Muslims became dominant, he's still portrayed as being borderline ascetic (he's described as mending his own clothes, forbidding the wearing of silk, forbidding the use of golden dinnerware and other ostentatious acts).

He lead fighters at Uhud and Badr, but I don't recall anyone ever taking of him being in personal combat (unlike Ali or Hamza his son in-law and uncle respectively).

He did have slaves (Zayd ibn Harith for instance) but a great deal is made about how well he treated them (he adopted Zayd) rather than "Look how wealthy our Prophet was, dude had a thousand slaves!"

Sources: Martin Lings' Muhammad:His Life Based on the Earliest Sources is not super scholarly, but for an accessible "how do Muslims view Muhammad" book I highly recommend it. The Venture of Islam by Marshall GS Hodgson is dry but a fantastic resource. Since the skeptical turn, most writers are silent the character of Muhammad, but you can find translations of Pseudo-Sebeos online. He was an Armenian historian writing just after Muhammad's death and confirms several details of the Muslim narrative.

Full disclosure: I'm not a professional academic. I am a Muslim. Take grains of salt as needed.

Part of the difficulty in answering this question is that there is no consensus. As /u/joathrowaway has noted, some scholars prefer to be more sceptical of the sources, others less so. /u/cptbuck has written an excellent survey of the issues here, which should be helpful.

As someone firmly on the revisionist/sceptical wing of the debate, I am nonetheless still certain he existed and from what we do know, Muhammad was an eminently capable leader, both charismatic and politically astute enough to build a new movement on the edge of two world empires. In this comment I discussed how this fits together, in particular quoting a 'barebones' account of what some historians think about Muhammad - the details unfortunately are still disputed.

We do have some early non-Muslim sources, but the picture is still murky. From a faded Syriac note, perhaps the first reaction (that we know of) to the Arab conquests:

... many villages were ruined with killing by [the Arabs of] Muhammad and a great number of people were killed and captives [were taken] from Galilee as far as Beth.

From an anonymous chronicle tentatively attributed to Thomas the priest (c.640):

In the year 945, indiction 7, on Friday 4 February (634) at the ninth hour, there was a battle between the Romans and the Arabs of Muhammad

From the Teachings of Jacob the Newly Baptised (perhaps written as early as 634, but could also have been written decades later):

Justus answered and said, “Indeed you speak the truth, and this is the great salvation: to believe in Christ. For I confess to you, master Jacob, the complete truth. My brother Abraham wrote to me that a false prophet has appeared. Abraham writes, ‘When [Sergius] the candidatus was killed by the Saracens, I was in Caesarea, and I went by ship to Sykamina. And they were saying, “The candidatus has been killed,” and we Jews were overjoyed. And they were saying, “A prophet has appeared, coming with the Saracens and he is preaching the arrival of the anointed one who is to come, the Messiah.”

And when I arrived in Sykamina, I visited an old man who was learned in the scriptures, and I said to him, “What can you tell me about the prophet who has appeared with the Saracens?” And he said to me, groaning loudly, “He is false, for prophets do not come with a sword and a war-chariot. Truly the things set in motion today are deeds of anarchy, and I fear that somehow the first Christ that came, whom the Christians worship, was the one sent by God, and instead of him we will receive the Antichrist. Truly, Isaiah said that we Jews will have a deceived and hardened heart until the entire earth is destroyed. But go, master Abraham, and find out about this prophet who has appeared.” And when I, Abraham, investigated thoroughly, I heard from those who had met him that one will find no truth in the so-called prophet, only the shedding of human blood. In fact, he says that he has the keys of paradise, which is impossible.’ These things my brother Abraham has written from the East.”

As you can see, these sources are not great for telling us anything about Muhammad's life, and everything they do say had been filtered through the perspectives of the three authors. We should therefore read these sources very carefully and I suggested an interpretation in this answer here, which also covered early Christian attitudes to Islam more generally.

As for pseudo-Sebeos (c.660), who has already been mentioned, we also have to be cautious. Since although his account matches several aspects of the traditional narrative of the Prophet's life, it also differs significantly on other points, for instance noting the role played by Jews:

Taking desert roads, they [Jews fleeing Christian persecution] went to Tachkastan, to the sons of Ismael, summoned them to their aid and informed them of their blood relationship through the testament of scripture. But although the latter were persuaded of their close relationship, yet they were unable to bring about agreement within their great number, because their cults were divided from each other.

At that time a certain man from among those same sons of Ishmael whose name was Mahmet, a merchant, as if by God’s command appeared to them as a preacher [and] the path of truth. He taught them to recognize the God of Abraham, especially because he was learned and informed in the history of Moses. Now because the command was from on high, at a single order they all came together in unity of religion. Abandoning their vain cults, they turned to the living God who had appeared to their father Abraham. So Mahmet legislated for them: not to eat carrion, not to drink wine, not to speak falsely, and not to engage in fornication.

He said: ‘With an oath God promised this land to Abraham and his seed after him for ever. And he brought about as he promised during that time while he loved Israel. But now you are the sons of Abraham, and God is accomplishing his promise to Abraham and his seed for you. Love sincerely only the God of Abraham, and go and seize your land which God gave to your father Abraham. No one will be able to resist you in battle, because God is with you.'

From this account, we would perhaps learn that Muhammad had sought to conquer Palestine first and foremost, a very different motivation compared to that provided by later Muslim sources.

Making sense of these sources is difficult, and I won't pretend that I can provide an answer. However, I hope that I have illustrated the important debates on this topic. New research is happening all the time, so hopefully in the future we can write more confidently about the life of Muhammad!