"The battle was over. On a stretch of high ground in the midland heart of the kingdom twenty thousand men had met in fierce, clumsy combat, and the day had ended in the decisive defeat of the stonger army. Its leader, the King, had been killed fighting heroically, and men had seen his naked corpse slung across his horse's back and borne away to an obscure grave. His captains were dead, captured, or in flight, his troops broken and demoralized. But in the victor's army all was rejoicing. In following the claimant to the throne his supporters had chosen the winning side, and when they saw the golden circlet which had fallen from the King's head placed upon their leader's, their lingering doubts fled before the conviction that God had blessed his cause, and they hailed him joyously as their sovereign.
The day was 22 August 1485; the battlefield was to be named after the small neighboring town of Market Bosworth; the fallen King was the third and ablest of English monarchs who bore the name Richard; and the man whom the battle made a king was to be the seventh and perhaps the greatest of those who bore the name Henry." - S.T. Bindoff Tudor EnglandPROLOGUE: 1485

By 1485 the War of the Roses had been raging in England for many years between the Houses of York and Lancaster. The Lancastrian Henry later took for his bride Elizabeth of York thereby uniting the houses.

The real matter was decided on the battlefield, at the Battle of Bosworth Field. It was here that Henry and his forces met with Richard III and Henry won the crown. (see quotation above)
The main problem facing Henry was restoring faith and strength in the monarchy. He also had to deal with other claimants, with some of them having a far stronger claim than his own. To deal with this, Henry strengthened the government and his own power, at the expense of the nobles. 
Henry also had to deal with a treasury that was nearly bankrupt. The English monarchy had never been one of the wealthiest of Europe and even more so after the War of the Roses. Through his monetary strategy, Henry managed to steadily accumulate wealth during his reign, so that by the time he died, he left a considerable fortune to his son, Henry VIII.

It could be debated whether or not Henry VII was a great king, but he was clearly a successful king. He had several goals that he had accomplished by the end of his reign. He had established a new dynasty after 30 years of struggle, he had strengthened the judicial system as well as the treasury and had successfully denied all the other claimants to his throne. The monarch that he left to his son was a fairly secure one and most definitely a wealthy one.

Henry had seven children by Elizabeth of York, four of whom survived infancy: Arthur, who died shortly after his marriage to Katherine of Aragon (a point of some importance during "The Divorce"), Henry, Margaret and Mary.
 
 

A Description of Henry VII

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A bust of Henry VII

His body was slender but well built and strong; his height above the average. His appearance was remarkably attractive and his face was cheerful, especially when speaking; his eyes were small and blue, his teeth few, poor and blackish; his hair was thin and white; his complexion sallow. His spirit was distinguished, wise and prudent; his mind was brave and resolute and never, even at moments of the greatest danger, deserted him. He had a most pertinacious memory. Withal he was not devoid of scholarship. In government he was shrewd and prudent, so that no one dared to get the better of him through deceit or guile. He was gracious and kind and was as attentive to his visitors as he was easy of access. His hospitality was splendidly generous; he was fond of having foreigners at his court and he freely conferred favours of them. But those of his subjects who were indebted to him and who did not pay him due honour or who were generous only with promises, he treated with harsh severity.
He well knew how to maintain his royal majesty and all which appertains to kingship at every time and in every place. He was most fortunate in war, although he was constitutionally more inclined to peace than to war. He cherished justice above all things; as a result he vigorously punished violence, manslaughter and every other kind of wickedness whatsoever. Consequently he was greatly regretted on that account by all his subjects, who had been able to conduct their lives peaceably, far removed from the assaults and evil doing of scoundrels. He was the most ardent supporter of our faith, and daily participated with great piety in religious services. To those whom he considered to be worthy priests, he often secretly gave alms so that they should pray for his salvation. He was particularly fond of those Franciscan friars whom they call Observants, for whom he founded many convents, so that with his help their rule should continually flourish in his kingdom, but all these virtues were obscured latterly only by avarice, from which...he suffered. This avarice is surely a bad enough vice in a private individual, whom it forever torments; in a monarch indeed it may be considered the worst vice, since it is harmful to everyone, and distorts those qualities of trustfulness, justice and integrity by which the state must be governed.