I have some changes I make to standard D&D equipment.
Slings should have a better range than the rules say. I change it so that when using a cast bullet, designed for usage in a sling, the range is the same as that of a shortbow. I believe the evidence shows that as a valid correction. When using a found stone, the distance is half of that of a shortbow, due to the random characteristics of the rock.
Foraging for stones, when the terrain makes it possible, requires a successful investigation roll. If successful, one stone per point above the DC per minute spent is retrieved. In most situations the DC would be very low, indicating a high probability of finding suitable stones.
A character may craft a sling in an hour using 5 copper pieces of material. Scrounged material can be used instead of spending money, but it won't be usable long term.
Regular (lead) bullets may be purchased in most towns at a cost of 4-5 copper pieces for 20 bullets.
Silver bullets might be available in marketplaces in larger towns at a cost of 5 SP/bullet.
Bullets can be cast from metals such as lead or silver using a Sling Bullet Molding Set. A Sling Bullet Molding Set costs 1 gold piece, weighs two pounds, comes with a 5-bullet mold, a ladle for pouring the molten metal, and a small pot to melt the metal in. It can be used to make lead and silver bullets for slings. One lead bar (2 CP, 1.5 lbs) can make 20 bullets in 10 minutes. Silver bullets can be made at a cost of four silver pieces per bullet.
A competent blacksmith can make a bullet molding set in a day. A blacksmith with competent business skills should be able to craft one in a few hours for a higher price.
Note: One and a half pounds (the weight of 20 lead bullets) is 24 ounces. Coins are typically 1/3rd of an ounce, so since each bullet is 1.2 ounces, it will take 4 coins to make one bullet. Lead and tin can be melted in a typical wood fire, but other metals such as iron, steel, silver, and gold must be melted in a forge.
Wielding a spear two-handed adds the Reach property. This better reflects the reality of using a spear to control the area around the user.
A character with proficiency in Smith's Tools can use them to craft a spearhead. A character with proficiency in Carpenter's Tools or Woodcarver's Tools can use them to craft a shaft that can be attached to a spearhead. It takes both to make a spear.
The total cost to craft a spear is 10 silver pieces, and 50 spears can be made in a week. The materials are likely to be easily procured. To craft a single spear would take a couple of hours. If two separate characters are crafting the spearhead and the shaft, the time is cut in half.
The spearhead crafting time assumes the use of a typical forge. If there is no forge available then the time is quadrupled as a crude forge, at a minimum, must be built and using a crude forge takes longer.
A character proficient with Smith's Tools and Arcana may use the spleen of a troll, as well as 500 GP worth of other supplies, to craft a +1 spear. It will take two weeks and a successful DC 8 Arcana check, with a lookup on the Crafting Complications table if they roll a 1.
While short swords were used in older times, most folks living in areas where the Norse were would mostly use a seax instead of a short sword that looks like a Roman gladius. For D&D purposes we consider a seax as being mechanically the same as a short sword, although they are single edged and more utilitarian.
Basically any character from Scandinavia who would normally be created with a short sword as one of their weapons would instead have a seax.
The full swords typically used by the Vikings who could afford them would be classified as longswords in D&D, but their hilts aren't long enough to be used two-handed.
The shields that the vikings used were boss-grip round shields. They aren't super durable but they are light, easy to use, versatile, and cheaply replaced.
Padded armor is cheap and ubiquitous. In France during the middle to late medieval period this sort of armor would be called a Gambeson. From what I can find, during the early Viking age it would be called a Kaftan or vápntreyja.
Most people during the Viking age were simple farmers. Even those who went on raids typically farmed most of the year and just used the summer to raid. There weren't a lot of rich folks, and especially in the early Viking age a lot of the more costly or complex items would be out of reach. Very few would be able to afford a chainmail hauberk, for example.
I have created a series of Backgrounds that fit the Viking age better than the standard D&D backgrounds. Unless they have a compelling reason, complete with a reasonable backstory, I expect the players to choose from mine when creating their characters. Most of their starting equipment should be based on their chosen background.
Most of the standard D&D classes can be at least rationalized into a Viking age campaign, even if many of them don't quite fit.
In the real world the only playable race is human. In a campaign with adult players I would tell them I expect them to play mostly humans. However, most of my players are kids that are new to D&D so I accept that Elves, Dwarves, Tieflings, Dragonborn, and even Warforged characters can exist.
So, other than the equipment available, I allow players to use almost any standard D&D character creation options - even though that isn't fully historic.
The typical Scandinavian of this era might wear turnshoes, socks made by nalbinding, loose fitting but not baggy pants, winingas (also known as puttees or leg wraps), a tunic, and one or more thin belts. Their clothing would be made of wool or linen for outer layers and linen for inner layers. They might have a hood for inclement weather and mittens for really cold weather.
They didn't have buttons and buttonholes, and their shoes didn't have shoelaces. Their clothing didn't have pockets, so they used pouches and bags hung from their belt.
Some character options just don't make sense historically, so unless the player can come up with a compelling reason why their character should have these options, they would not be allowed to choose them.
One good example is plate armor. That wasn't invented until long after the Viking age, so that isn't an option in my Viking era campaigns. The same applies to greatswords, also known as Zweihänder, claymore, spadone, and the like.
There is other equipment available than what I allow at character creation, and the players will likely get chances to get them later. For example, while crossbows are not available when starting, they did exist and the Norse would have known about them. But their construction techniques and cost as well as cultural biases meant they were not used often in Scandanavia - however, those traveling would see others use them and be able to trade to get them if they wanted.