Depictions showing handguns carried at the shoulder like pikes and other weapons often were show up pretty early on and generally remains the norm for centuries. Aside from tools for cleaning and mending their weapons, each soldier would have needed a pouch containing bullets and leather or cloth patches to wrap them as well as a flask of powder. Some arquebusiers might also have carried multiple smaller flasks, each with a pre-measured gunpowder charge ready to use, but the exact details are unclear and likely varied from man to man. In the early 15th century, instead of a match, some handgunners instead still used to light their piece using a red hot iron rod like artillery was, which would have required staying close to an open fire and was likely part of the reason firearms continued to be mainly used in the defense of stationary positions until the growing popularity and user-friendliness of matchlocks started to make them more mobile. When possible leaving their firearms in some sort of cart or wagon was definitely preferred, especially with some of the heavier ones. The heavy musket introduced in the 16th century could weigh 20 lbs or more and a number of writers mention that it was very tiring for infantry to carry long distances by themselves.

https://imgur.com/UGk9i9g Here are a couple of Swiss depictions from 1483 which show one arquebusier hanging his powder horn from his arquebus as he carries it and another one with his pouch on the ground as he loads his weapon.

As for slings, they generally don't show up on depictions of infantry in the 16th and 17th centuries, but by 1600 they do seem to have become the norm for cavalry. This illustration by Walhausen shows two different types of slings in use: the dragoon carries his matchlock musket slung across his back to use after dismounting while the mounted arquebusier/carbinier carries his weapon muzzle down near his hip on a "swivel sling" so that it can be more easily used from horseback.

Let me know if you have any follow up questions.