Though what weapon you use is ultimately down to what you find most fun. But, some weapons are definitely better. Weapon choice is down to three main factors: Rarity, Perks, and Quality.
Rarity[]
Rarity is by far the easiest factor to figure out. The higher the rarity, the better the gun, but it is by no means the most important. A level one Legendary will be worse than a level 20 Rare, and an Epic with good perks is better than a Legendary with bad perks. Rarity is important, but is by no means the most important.
Perks[]
Perks are arguably the most important part of a weapon, and they will become even more important with the release of the Perk Recombobulator. It is hard to evaluate a weapon's perks, but u/Whitesushii made a reddit post that covers the topic and makes it easy to understand. You can find it here: https://www.reddit.com/r/FORTnITE/comments/89gsmb/guide_to_perk_priorities_and_identifying_great/
Quality[]
Quality refers to the general effectiveness of the weapon not based on their perks, rarity, and level. Some weapons are just better than others, and knowing what is good can help you improve your combat effectiveness. Here is a list of the weapons that are considered to be the best by the community.
Assault Rifles[]
Shotguns[]
Snipers[]
Pistols[]
Explosive Weapons[]
You may be noticing a lack of Melee Weapons. The reason for this is, though they can do a lot of damage, they are much less efficient than Ranged Weapons, even in the hands of a Ninja. When you eliminate a target with a Ranged Weapon, you can immediately snap to the next one with little to no delay. When using a Melee Weapon, you must run to the next target after killing the first one, making it take much longer. Additionally, when using a Melee Weapon, you are much more vulnerable to husks, as you must get close to them to kill them, and when you are close to them they can also hit you.