Before the nineteenth century, Russia was arguably the only country with whom the Qing empire had formalised foreign relations, with this formalisation taking the form of two treaties, the first signed in 1689 during the early reign of Peter I as Tsar of Russia, the second signed in 1727, two years after his death. While I can't speak to the Petrine side of the equation, particularly as regards his thoughts on China, I can say a bit about these two treaties and their respective backgrounds.
The Russians had attempted to make contact with China, then under the rule of the Ming Empire, via Mongolia as early as 1608, and a diplomatic mission reached Beijing in 1618 but was turned away. Sustained contact with a 'Chinese' state began not with the Han Chinese Ming via Mongolia but with the Manchu Qing via Siberia and Manchuria. In 1643-6, Vasily Poyarkov and a dwindling band of men travelled along the Amur River, antagonising local tribes who were by and large clients of the Qing, and in 1650-2, Erofei Khabarov engaged in a more deliberate raiding campaign against Qing allies in the region. This seems to have drawn the attention of the Qing, who had by and large wrapped up their conquest of China from the Ming, and over the course of 1654-8 a force of Qing and Korean troops intercepted and fought back a third raiding campaign led by Onufry Stepanov. After Stepanov's death in 1658 the Qing-Russian engagement on the Amur settled into more of a cold war, with contests over the loyalties of local chiefs punctuated by the occasional frontier raiding.
The series of escalating events that eventually culminated in the Treaty of Nerchinsk began in May 1683, a year after Peter's accession to the Russian throne. The Kangxi Emperor, who had recently put down the Revolt of the Three Feudatories and was close to conquering Taiwan from the last Ming remnants, offered to discuss peace terms with Russia on the condition that the Russians abandon their palisade fort at Albazin. Receiving no response, the Qing assembled an army and razed the fort in June 1685, although it turns out that the slow pace of communications meant that Kangxi's message was still in transit, and arrived in Moscow five months later. The Russians prepared a dual response: first, a plenipotentiary official, Fyodor Golovin, was sent out in January 1686 to stabilise the situation; second, a small corps of troops and engineers was sent to re-establish the fort at Albazin, possibly as a bastioned earthwork rather than as a palisade as before. Albazin was besieged again in July 1686 and was starved into capitulation by the end of the year, so Golovin arrived at the Russian forward base at Selenginsk in October 1687 prepared to discuss peace terms.
This, however, is where the story gets complicated, because the Qing-Russian relationship was never purely bilateral. Lying between the Qing and Russian empires was the Mongolic steppe, where a number of smaller polities had risen and fallen in the years since the collapse of the Yuan, and which would see their roles shift substantially when sandwiched between the two empires. The biggest success story of the period would turn out to be the Zunghars, an Oyirad tribe based in what is now northern Xinjiang which, by the end of the 1680s, had come to dominate most of the Oyirad tribes (excluding the Khoshuts, who migrated to Tibet, and the Torghuts, who migrated to the Ciscaucasian plain). Under the leadership of Galdan, the Zunghars turned their eyes eastward, aiming to bring the autonomous Buddhist monasteries of Mongolia under the authority of Galdan's patrons, the Gelug sect led by the Dalai Lama. Galdan began his war against the eastern Mongols in 1688, scattering many of the tribes and driving some into Qing territory, and some into Russia. Whereas those that entered Qing lands were quickly made to swear fealty to the emperor, the sparsely-populated and thinly-defended Russian frontier instead became the target of raiding, and Golovin was driven out of Selenginsk by Khalkhas fleeing Galdan's attack. Only after Galdan's campaign quietened down and the frontier stabilised did the Qing and Russians meet at the table.
The intervention of Galdan had created a new issue for the Qing and the Russians, as the upcoming talks would have to decide not only how the Qing and Russians interacted directly, but also the question of how the two states would operate in Mongolia with reference to each other's activities. Which makes it interesting that the authoritative version of the treaty did not use Mongolian (which both sides would have translators for) as the intermediary language, but Latin. The Qing's Jesuit courtiers would here, as in many other Qing activities, be employed as direct agents of the imperial will, and communicate directly with the one or two classically-educated members of the Russian delegation. The Russians had originally hoped to retain as much control of Siberia as possible, but the simple fact that the Qing could muster about 12,000 troops against the Russians' 1,500 – and actually started doing so when the Russians appeared to be trying to get out of negotiations – forced their hand. The treaty, signed at Nerchinsk on 27 August 1689, had the following stipulations:
While the explicit terms are quite simple, there are, as Peter Perdue suggests, some underlying implications. Namely, the permission to trade essentially created an economic incentive for the Russians not to rock the boat with the Qing. Selling Siberian furs to the Qing would require far less time and cost of transport than trying to get them all the way to European Russia, creating a lucrative frontier commerce. In exchange, it was heavily implied that the Russians were not to sponsor anti-Qing proxies, because the Qing would find out one way or another. Galdan had hoped to secure an alliance with Russia against the Qing, but found in 1690 that Golovin was no longer interested: Russian priorities were maintaining trade with the Qing, maintaining control of their remaining Mongolian clients, and maintaining the safety of Russian subjects. Galdan repeatedly petitioned the Russians but was turned down, the Kangxi Emperor having noted to the Russians that any support for the Zunghars would be interpreted as a violation of the Treaty of Nerchinsk.
In one sense, neither the Qing nor the Russians necessarily explicitly treated each other as equals: both were relatively used to operating in hierarchical terms, and rivals of parallel status to themselves were somewhat difficult to reconcile, not necessarily due to inherent cultural bias so much as the threat this posed to the systems of hierarchy they were trying to establish on their frontiers: after all, if you were paying tribute or offering military service to an overlord of self-declared supreme status but which recognised another of equal status, what, ideologically, stopped you from switching overlords once in a while? Or better yet, declaring yourself one? However, the uncertainty created by the Zunghar ascendancy and the mediating role of Western Europeans in the negotiation process created a framework of de facto equality.