There are a very great number of primary sources for the Mongol Empire, especially given the time period- as is only natural for an empire spanning two continents and a large number of sedentary, literate societies. The problem is that it's rather hard to access these, given the dearth of translations- particularly affordable ones.

The fact that there are dozens of sources in dozens of languages means that most historians of the Mongol Empire tend to focus on a specific region (usually China or Iran, as they have the most sources), which should mean that plenty of translations so that historians who read Persian can understand Chinese sources, and vice versa. However, largely because of the perpetual dearth of scholarship of non-Western, pre-Modern history, this has not really been the case. There are some translations into English, but these are often hard to find or are atrociously expensive to acquire (or, more usually, both).

There were two native Mongol sources written: The Secret History, of course, and the Altan Debter. The Secret History is still very much extant, although the only surviving form is a Chinese transliteration of the original Uighur script. A number of good translations in English are available; the most scholarly is Igor de Rachewiltz's, although if you want something more readable then Urgunge Onon's version. The Altan Debter, however, is now lost to us in a direct form; it is often to considered to have been more a collection of small Mongol histories and fragments, if I remember correctly. There are some histories which we do have, however, which cited and heavily relied on the Altan Debter; these are our most important sources on early Mongol history aside from the Secret History.

These are Rashid al-Din's "Jami al-Tawarikh", usually translated as "Compendium of Chronicles" or "Collected Chronicles", and two Chinese histories, the "Yuan-shih" (the official history of the Yuan, written in the Ming dynasty, as was the custom in Chinese historiography) and the "Shenwu qinzheng lu" (the spelling may vary on this on a lot). Rashid al-Din's history is particularly noteworthy, as it is excellently written and considered the first true "world history", as he deliberately used native accounts of the nations he wrote about to create a much more accurate and wide-ranging history than had ever been attempted before.

The trouble with all these sources is that there are no acquirable translations. The Yuan-shih and Shenwu have not, to my knowledge, ever been translated into English; and while there is a translation of the portion of the Jami al-Tawarikh concerning the Mongols into English (done by the great Wheeler Thackston), it is virtually impossible to find a copy anywhere. I eventually found a version of Amazon, bundled together with two other Mongol chronicles which costs several hundred pounds, which is not ideal.

Nonetheless, there are other important sources with more easily affordable translations. Juvaini's "History of the World Conqueror" is an important Persian sources, and there is a translation by John Boyle which is quite easy to attain. There are other such Persian histories, such as those written by the virulently anti-Mongol Juzjani and Ibn al-Athir (the latter's history also covers a lot of stuff about the Crusades and the like); in addition to later histories, usually specifically pertaining to the Ilkhanate, such as Qashani's history. There is also Wassaf, whose history is, I believe, quite wide-ranging, but is written in such intolerably impenetrable Persian that it is rarely used. To my knowledge (which is extremely limited), there are no English translations of Wassaf, Juzjani or Qashani, although there is one (somewhere) of Ibn al-Athir's history. There's also a history written by the Nestorian Christian bishop Bar Hebraeus, which includes some important stuff on the Mongols, and has a good English translation.

There are also various travellers accounts- you say you've already read Marco Polo (naturally) and the Mission to Asia, which I think includes William of Rubruck's important account. There is also the account of Plano Carpini, which is worth a read, and the "Travels of an Alchemist", which details the visit of a Taoist monk, Changchun, to Genghis Khan; this is particularly notable for its first-hand account of Genghis.

There are more, but those are all that I can think of off the top of my head. A lot of these may be hard/expensive to acquire, but some are not, and all are useful and interesting reads.

In terms of secondary sources, I'd urge caution- you're likely to be pointed in the direction of Jack Weatherford's book, which is a good read but somewhat dubious in terms of historicity. David Morgan's "The Mongols" remains the standard introduction lecturers would likely recommend (although it is a tad brief), while Paul Ratchnevsky's "Genghis Khan: His Life and Times" is still the standard biography of Genghis, and is a truly excellent book. Those stand out as good introductory secondary works on the empire as a whole; I can recommend a few more detailed works on specific places/aspects of the Empire, if you want.

I don' thave anywhere near the expertise to give you a really satsifying answer, but I would suggest looking at Chinese texts from the period if you can find them.

The Mongols played a huge role in chinese history and I am sure that Chinese historians have primary accounts of the mongol conquests and of the Mongol Yuan Dynasty.

Secondaries:

The Mongol Conquests in World History - May, T.

A good book that covers the chronlogical history of the Mongol Empire starting with Genghis' unification to the retreat of the Mongols to their eventual retreat into Mongolia. It also talks about the short and long-term impacts of their rule as well as several other outcomes due to their administration efforts. Like most modern texts dealing with the Mongols, it views them through a much more objective lens (as opposed to earlier sources that still very much referred to them as barbarians). Readable as well.

Genghis Khan and the Making of the Modern World - Weatherford, J.

I've said this before -

a rather refreshing breath of literature in that it dealt with his life in a much less downgrading fashion by attempting to paint him in a positive or at the very least neutral light. A piece of revisionist history, sometimes hyperbolic in fashion, as well as glossing over a few facts that are true, most likely because they didn't fit the image of the Khan being a civilised, peace-bringing lawkeeper that the book suggests.

Weatherford's book however does have some stories based off anecdotal evidence, as well as some inconsistencies, however on the whole it's another readable book that has a good approach towards the Mongols.

You can also check out AH's booklist where you'll find some books on the Mongols here.

Thank you for your responses. I appreciate your help!