The Swedish army of the time, both the earlier Carolean one and the later one during the Liberty Era and the era of Gustavian absolutism had two types of regiments.
There were mercenary/professional ones, värvade (meaning "recruited"), which included permanent garrisons in Sweden's fortifications and provinces, including the German provinces (Bremen and Swedish Pommeriania pimarily) and in Estonia and Livonia (today part of Estonia and Latvina), the royal guard and the artillery regiment.
The second category was the indelta (meaning "subdivided") regments. These were based out in the counties part of the Crown of Sweden and had peasants divided into rotar or in the case of cavalry, rusthåll in which farms and their self-owning peasants were in exchange for protection from conscription (which had been used extensively dring the 17th century) and taxes were required to provide both a soldier, a croft for him and his family to live on and his equipment (from state factories).
There were no centralised conscription agencies going through recruits and assigning them to various units and services. Instead, men applied directly to the regiments (in the case of the värvade ones) or were found by the peasants required to provide a soldier. You could always make contact with an officer or peasant heading the rote or rusthåll and declare your interest to join. In peacetime, this could mean some serious scrutinity. The officers and peasants resposonsible for providing men could at times be picky - you needed to be of a certain age, hale and hearthy, of fine health, have no serious physical disabilities, be of a minimal stature and not wanted for any crime. In wartime, things would be easier of course, as the need for warm bodies were never ending.
The peasants usually recruited locally among family and friends of family. The second or third son of a peasant or crofter part of the rote or rusthåll was a common recruit. Soldiers, at least during the Carolean era, lived and worked close with their officers and officers were required to see to the welfare of their soldiers and make sure the peasants of the rote or rusthåll filled their obligations and provided what they should and did not force the soldier to more than the required corvee labour in exchange for the croft and so on. Soldiers also travelled to train and met with other soldiers and officers. They were thus often more well-travelled than the normal countryside denizen and often had "friends in high places" in the form of their (often noble) officers which they would socialise with during training, drill and exercises. Add to that a snazzy uniform and high-quality equipment and becoming a soldier could be a step up socially for crofters and the like on the countryside, so the regiments had no real problems filling positions during peacetime and even during the early years of the Great Nordic War. You would have at least some competition wanting to join.
So, rather than get assigned somewhere, you would apply to a regiment and hope to gain a position there, and you would apply to a regiment of the type you wanted to join. This was the case of a young but not very rich Mecklenburgian nobleman who applied to and joined Hussarregementet, as a Kornett (the lowest officer rank, roughly 2nd Lieutenant) in the värvade Swedish hussar regiment in Pommerania in 1758, partaking in the Swedish participation in the 7 years' war and the attempt to regain part of Swedish Pommerania from Frederick the Great's Prussia. He was captured by Prussian Hussars in a skirmish, who were duly impressed by his fighting ability and recruited him into their own regiment. His name was Gebhard Leberecht von Blücher and he would end his career as a Field Marshal rushing to aid Wellington at Waterloo 1815.
In 18th century Britain, you enlisted into the regiments. A man could often find a recruiting party in his town's tavern of a certain regiment. The infantry used this tactic throughout the century as a popular means of gaining recruits, not so much conscription - even in war time. Britons revolted a few times from the conscription acts placed in the wartimes of the 18th century. By 1775, the British army had 70 regiments stationed around the empire, from the home islands, to Ireland, to America/Canada, the West and East Indies, and Africa. The cavalry mostly stayed in the Isles and the artillery had mostly stayed in England. A man usually be recruited in most regiments.
Soldiers were not usually assigned to the different branches like today. Rarely, when in war, the branches would take whatever recruit was coming their way. During the outbreak of the American Revolution, the British army had trouble filling out their artillery companies to full strength at forts or garrisons. The artillery leaders took drafts from the infantry to fill out the numbers, something done by all European armies, and get them to the full strength needed. This also happened with the navy in some cases. Maritime Canada had to use regular infantry as drafted marines and sailors. Most of the time it was a temporary task until that unit got the regular reinforcements but not all the time. It would depend on where the men needed to be sent to.
However, the British army did have some ways that they assigned soldiers to certain units that required experience and aptitude of an excellent soldier. Foremost, the flank companies of an infantry battalion. Ten companies made up a British battalion. Depending on the years it could be between fifty to a hundred men. Out of the ten companies, the flank companies comprised of two of them - the Grenadier and Light companies. To get into these companies you had to show yourself worthy of it, as they would be in realm of elite troops. They got the same training as other companies but also more. Grenadiers had the role of shock troopers. In the later seventeenth and early eighteenth century they carried bags of grenadiers and wore tall caps that could be made of bearskin, metal, or decorated wool. They also carried swords in some cases. Armies used to them to break up lines and punch through for the rest of the infantry to follow. The armies also required grenadiers to be tall, around six feet, and strong so that they can toss the grenades far. The grenading part of their role diminished towards the end of the first quarter of the eighteenth century as the grenades were dangerous to use still and had caused casualties on their own sides. The light infantry came about in the middle of the century during the Seven Years War. They were designated as skirmishers to harass the enemy lines and be quick to retreat. They also had to be excellent marksmen. Regimental officers wanted the flank companies to comprise of experienced men that fit the requirements. A year of experience was often enough and a soldier could enter once a spot opened up, whether from promotion, casualty, or transfer of another soldier.
Thomas Simes did write a bit about how to distribute new recruits in a battalion. A small aside, Simes was a military writer of the eighteenth century that wrote textbooks on military discipline and economics which both armies used in the American Revolution. He wrote:
Once new recruits had arrived at their regiment, they were proportioned out evenly to the battalion companies. The Flank companies were then allowed an equal compensation drawn from the battalion companies. For example, if 40 recruits were divided between the eight battalion companies at five per company, the Light Infantry company could then pick one man from each of five battalion companies as compensation, as would the Grenadiers. Which companies were to be subjected to this draft must have been regulated by a chart to ensure that no battalion company was picked more frequently than another. Officers of the Flank companies would choose the men that most nearly fit their ideals, with large, strong men going to the Grenadiers, and small, intelligent men to the Lights
Soldiers in the eighteenth century had some autonomy of what unit they wanted to belong to, save for the drafts that happened from low numbers. After the battles of Saratoga and the surrender of Burgoyne's army under the Convention, the Britsh army lost quite a bit of their strength in that. In addition, some regiments lost hundreds of their soldiers which left them with often times just a couple companies worth of men. These men would be drafted into other regiments, specifically in the Northern Army in Canada. Otherwise when a regiment lost their strength, they would embark back to England to reach full strength again or have additional recruiting companies in England while remaining in America.
Alexander MacDonald Letterbook, 1778.
Don Hagist, British Soldiers American War.
J.A. Houlding, Fit for Service.