The problem is, I can't seem to find much beyond a handful of sources such as the ones cited in the Wikipedia article and government programs like those seem rather grand and sophisticated for a state back then.

As with many such questions about early Islam, we're going to run into the historiographical problem of sources. As background for this it would be worth reading Robert Hoyland's excellent overview essay Writing the Biography of the Prophet Muhammad: Problems and Solutions (PDF). While this discussion is focused on the life of Muhammad, it serves equally well as an introduction to the problems in early Islamic historiography generally.

To summarize that discussion, however, our sources for the history of early Islam, broadly speaking, are as follows:

Contemporary Documentary Sources (i.e. sources for which we have some original or very early physical document that can be dated in a reliable way)

Among the most important of these we have:

• The Qur'an
• The Constitution of Medina
• Texts written by non-Muslims about early Islam
• Epigraphy (i.e. carvings and inscriptions, for instance on coins or on rocks)
• Surviving early texts, particularly papyri from Egypt, and often dealing with administrative affairs

Traditional sources (i.e. sources that were eventually written down, but for hundreds of years existed only as oral traditions, handed down by a supposed chain of narrators)

Among the most important of these are:

• The Hadith (sound and unsound, whether prophetic or about the companions)
• The Sira (biography of the prophet, e.g. Ibn Hisham, Tabari)
• The Tafsir (i.e. exegesis of the Quran)
• Other histories of the conquests and later periods (Tabari, Baladhuri, Waqidi).
• Literature: poems, songs, and prose that nonetheless claim to depict

This latter category of sources is deeply problematic. While they remain foundational texts of faith for believing Muslims, they have also come under sustained and withering criticism academic historians over the past century. Simply put, academic historians do not accept the evaluation process used by Bukhari, Muslim, etc. as being sufficiently rigorous so as to make reliable statements about the life of the prophet or the early period of Islam. This goes even more so for the other sources, many of which were not even accepted by early Muslims.

So Ahmed ibn Hanbal is widely quoted as saying:

"There are three branches of Islamic knowledge that are totally unfounded -- Tafsir, Malahim [i.e. apocalyptical literature] and maghazi [i.e. the prophetic raiding literature and by extension the Sira which is largely composed of maghazi]

Nor is there an easy way to extract some "kernel of truth" out of these flawed sources-- there is no hermeneutic for doing so without introducing substantial bias into the interpretation.

That's not to say such sources are uniformly without use: Tabari in writing about his own time is, of course, a documentary source. Sound hadith collections may not tell us anything about the prophet, but they may tell us quite a lot about what 9th century jurists like Bukhari thought about the prophet.

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All of that is historiographical background to what is one of the principle historical questions in Islamic studies, and one that has a critical bearing on the answer to your question, namely:

What was the nature of the early Islamic State?

Here we run into a problem. The traditional sources depict a highly organized, centralized state enterprise going back to the time of Muhammad himself. If we take on the source critical objections, however, a very different picture emerges.

Our documentary sources, on the other hand, including Non-Muslim texts and surviving papyri and other administrative documents from the early period of the conquests depict a chaotic array of local taxation schemes and systems, many of which are difficult to characterize as a "system" at all. Nonetheless, that taxes were collected on an extensive basis is not in doubt.

Moreover, this view deeply challenges some questions about the "Islamic" nature of the early Islamic State.

So, for instance, while "Jizya" by the start of the 8th century has taken on the meaning of "discriminatory tax on non-Muslims" there is no indication from our earliest sources that it meant anything other than "poll tax", virtually indistinguishable from those applied by the Byzantines or Sassanians.

Or Zakat, which is Quranic, but may not have been systematized until it became legally obligatory, effectively a tax, in the Ummayad period.

This is without getting into the fascinating, but not especially relevant to your question, discussions about Islam and what being a "believer" may have meant in the first century of Islam.

This is contrast to the strict legal doctines and uniform policies that we are told were put in place by the traditional sources.

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Perhaps the easiest way to understand this then, and which will segue into my next point, is that legal scholars were either universalizing a pre-existing ideal or else were imposing anachronistically their own ideological notions of what a state needed to do, or practical realities of what their state was then-doing, back onto the earlier period.

What's fascinating to me as someone who has interest both in this period and contemporary Islamist movements is that this is exactly what seems to have been in the Wikipedia articles you're reading.

So, what can we actually say was being done with these tax revenues that the early Islamic state was collecting? Well, per Fred Donner's Muhammad and the Believers:

The diwan was originally created under the ami r al-mumini n 'Umar as a register of those Believers who were entitled to receive a share of the booty and tax revenues that were in his day beginning to flow into Medina. The recipients at first included some who were not in the army (notably Muhammad's widows), but the bulk of those on the first diwa n were soldiers, who were entitled to a regular pay allotment—its level depending on how early they had joined up. As time went on, the di - w a n became almost exclusively a military payroll; eventually, the word diwa n came to be applied to other branches of a fledgling bureaucratic system, with the meaning of "government department"; hence we begin to see references to a chancery (the diwa n al-rasaV ) and a land-tax administration (diwa n al-kharaj) . The ami r al-muminin s also established something called the barid , or official courier system, through which they received reports from their governors and spies in the field.

This well-attested to system for distributing loot and taxation from the conquered territories seems to have been the basis for the distribution of alms for the poor, so Patricia Crone writes in Medieval Islamic Political Thought:

In the early centuries there seems to have been a conception of a system of regular government support for the poor and the invalid. This conception was rooted, not in the institution of obligatory alms or the fifth, but rather in the stipend system of the Umayyad period. Registered soldiers disabled in service would receive an invalidity pension, and some sources claim that similar provisions were made for the disabled and poor in general in Umayyad times.

She summarizes these systems by saying:

Precisely how much truth there is to them is debatable, but they do testify to a concept of what one might call a welfare state.

That, however, is a very far cry from an "Islamic socialism" that entails such complex state institutions as "unemployment insurance, retirement pensions."

Moreover, far from being universal, these benefits were directed at the most narrow elite of society imaginable: the muslim community that now found itself ruling over the vast riches of almost all of the Byzantine and Sassanian empires.

As I've written about elsewhere, most recently here, Islam in the early period does not seem to have been a universal religion; one could not simply convert and receive these benefits.

When Islam did universalize and begin to experience a large-scale conversions, that necessarily entailed what Robert Hoyland has termed a reduction in the "benefit package" paid out of the Diwan to soldiers and to Muslims generally, as well as an increase on the tax burden owed by Muslims.

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To return to my point about Islamists and reading this kind of thing backwards: to read 7th century saddaqa as being a guaranteed universal income strikes me as being as anachronistic as Muslim Brotherhood's slogan that "Democracy is Shura."

From a political perspective in making the case that the modern liberal welfare state is Islamically acceptable, that's fine. But the historical claim that therefore the early Islamic State was a modern liberal welfare state is untenable.

So, for instance, as much as I enjoy Shadi Hamid as a writer and thinker on issues of Islam and contemporary politics (and much of the claims being made in that wikipedia article seem to come from his essay here you can see that he is relying on a completely uncritical use of traditional sources to ultimately make a political point.

I'll include an additional bibliography in a part II as I'm about to hit 10,000 characters.