Warhammer: End Times - Vermintide

There are a few solutions available to you when it comes to acquiring a weapon of Exotic Rarity.

Unique - Red
Exotic - Orange
Rare - Blue
Uncommon - Green
Common - White

The First is as a Reward won from the game of chance at the end of every standard mission, Ranald's Bones. Of the eight possible rewards, Exotic's will begin to appear in the uppermost slots on the HARD difficulty and above, Nightmare will up those odds, dropping them as low as the 4th position and Cataclysm will again lower the position another space. Cataclysm will require you at minimum to roll a four or five before being able to claim an exotic from the game. Tomes, Loot Dice and Grimoires will all improve your odds by changing the Dice you play with, but this solution requires time and luck to retrieve your weapon.

The Second possibility is from the Bounty Board, Exotic's are a standard "Quest" Level Reward, requiring you to complete anywhere from 4-8 "contracts" to unlock the weapon. However, the board only becomes available once you have completed the final level (The White Rat), and requires you to return for several days as not every contract will be rewarded with a "Key" necessary to finish the quest.

The third, final and in my opinion quickest option, is to use the forge to fuse lower tier weapons into a higher tier. The way this works is ANY five weapons of the same tier, from any of your five characters can be combined into a weapon of a higher tier, from white to Green, Green to Blue, and Blue to Orange. The Weapon that is created uses a ratio based on the input of the weapons, their type and the character they originally belonged to, You can also substitute raw materials that correspond to the level of rarity needed, an example of this would be:

(4 Green Tier Dwarf Ranged weapons + 20 Green Gems = 1 Blue Dwarf Ranged weapon).

Additionally, you can use raw materials at the Shrine of Solace, using the option to "Pray" for the individual weapon by tier and type.

Material gems can be quickly won via the Last Stand Game Mode, Each Endurance Coin you pick up equates to SIX of the Material gems needed and appear every couple of rounds starting at round two. With the Veteran difficulty rewarding Green Material, Champion rewarding Blue, and Heroic rewarding Orange. A Mixture or combination of this last solution should allow you to pick up your first exotic before even beginning to sniff at the end game.

So, a few options are available for you, choose whatever one fits into your time frame you've set for yourself. The Exotic and Unique tiers and their traits will SIGNIFICANTLY lessen the difficulty you will have in every aspect of the game and are well worth the time spent. Good Luck!