The idea of living in a religiously motivated withdrawal from the world was fairly frequent amongst apoloistic preachers in 12th century France (e.g. Robert of Abrissell). Many of these figures seem to have fiercely rejected papal authority on the grounds of the corruption of clergy and as a reaction to the increasing wealth and 'wordly' power of the church, which was developing as religious authority became increasingly centralised at Rome. Preachers such as Robert of Abrissell reacted against this by practising near ascetism (going about barefoot, unshaven, wearing hairshirts, abstaining from meat, living amongst poor followers\prostitutes) and adopting poverty as a means of simultaneously exhibiting & embodying their highly reactive philosophies. The influence of Neo-Platonism upon many preachers at this time also fostered the perception of the 'material' world as corrupted and fallible. It could have been a small jump from accepting this philosophy to accepting poverty, the ultimate rejection of the material world. Though mostly justified in their loathing of wide spread corruption (simony) throughout the Catholic clergy, many of these figures (or their followers\successors) were eventually accused of heresy and didn't end up fairing too well.

It is, however, a pretty interesting example of how the rejection of worldly power (e.g. financial wealth, political influence) and acceptance of poverty appears in the Mediaeval world. A whole slew of adherants to this 'improverished ' anti-papal tradition are documented in France and the Lowlands, whilst persecution against them may have heralded the increasingly intolerant repression of alternative Christian philosophies\doctrines. R.I. Morre's 'The War on Heresy' focuses on the nature of 'heretical' movement in 11-12th centuries and details the important role that the issue of poverty, real and theatrical, had in its development. Not entirely helpful, but kind of interesting as a starting point.

Not sure if you mean people who take a vow of poverty or peasants, but I've recently been reading a bit on the Medieval views of the peasant class.

One thing that came up in my reading was the peasant's relation to God and salvation from the perspective of Christians at the time and the Catholic Church.

Here is an excerpt from Images of the Medieval Peasant, by Paul H. Freedman. You can find it in Google Books yourself, but I'll include a link at the bottom as well.

"Throughout the Middle Ages, however, noble saints dominated, especially north of the Mediterranean, while royal saints, although found all over Europe, were especially visible in the East. The figures changed somewhat after 1150, when movements advocating poverty, asceticism, and the apostolic life gained strength, but the almost magical quality of high birth, and the better renunciatory narrative that such rank created, meant that the peasantry made no significant dent in the noble domination of the beatified. If the peasant's way of life removed him from temptation, it also allowed him little opportunity for heroic abstinence.

Here one must distinguish between striking individual examples of renunciation and the basic spiritual condition of an entire class. The peasantry was widely considered to hold certain privileges with respect to salvation, but not with respect to individual spiritual distinction meriting sainthood. The individual heroic piety requisite to sainthood was manifest and dramatic when there was more to renounce. The aristocratic saint could on the one hand counter the prevailing violence and pride of his class and on the other hand gain saintly stature from attributed aristocratic virtues (noble bearing, restraint, or sternness), especially the high medieval saint, who was seldom the holy fool, hermit, or simpleton so prominent in desert monasticism and the Orthodox world.

But some peasants didi achieve sainthood, albeit proportionally few, as noted above. A Saint Wulfstan of the tenth or eleventh century (not either of the two sainted bishops of that name) died while cutting hay and so served as the patron of haymakers."

Here is the full link.

First of all, it seems to me that this books is making the supposition that we can see what and who those in the medieval Church valued and idealized by first looking at the types of people that were sainted from that time. Next, to answer your question, we need to analyze those saints who lived in poverty. The overwhelming evidence seems to suggest then, that from this criterion, it was those of noble birth who renounced their wealth that were more often saints than those who were born poor such as the peasantry. It seems to me that while the poor as a class were somehow close to God because of their poverty, they lacked the virtues necessary to gain high distinction because they had no temptations to renounce. On the other hand, while the nobility were often violent and proud, it was because of these temptations and the renouncement of them that gave them the opportunity to soar above the rest on an individual basis In other words, what matters most seems not be who was poor simply by fact, but rather why and how one was poor.

Poverty became a controversial topic in the high Medieval period, as evidenced by the disputes over the alleged poverty of Jesus and the disciples. The rise of the Franciscan order in the 13th and 14th centuries generated a number of arguments and disputations. A great deal can be learned by reading a biography of St. Francis; I would recommend St. Francis: A New Biography by Augustine Thompson (Cornell, 2012). For a primary source, see the works of St. Bonaventure, particularly his Apologia pauperum (trans: Defense of the Mendicants, The Franciscan Institute, 2010). His writings represent a matured, Franciscan position on poverty, and they serve as a good locus for comparing with other periods of history.

By way of an answer, the church did not idealize poverty the way we would understand it today, if at all. Charity, not poverty, is listed by St. Paul among what came to be known with St. Aquinas as the theological virtues (the other two are hope and love). Poverty was a nebulous concept, and the extreme form of poverty advocated by St. Francis that today defines our understanding of the term, was hotly debated. He and the later Franciscans held that Jesus and the Apostles lived in complete poverty, owning nothing, and this became the subject of many theological debates. That St. Francis and the Franciscan Order were so controversial can tell us something about the way that poverty was viewed in the Medieval period. Their teachings, marked a distinct change in the way the church related to and tolerated poverty as an ideal.

To gain the perspective you're seeking, I would suggest contrasting the works I mentioned with Peter Brown's recent book on wealth and poverty, titled Through the Eye of a Needle: Wealth, the Fall of Rome, and the Making of Christianity in the West, 350–550 AD (Princeton, 2012). His provides a very thorough look into the notion of poverty from the end of the Patristic era and into the earliest years of the Middle Ages.