In Prey, you can use many different kinds of weapons. A list of the most important ones that can be obtained early in the game can be found in the "Where to find basic weapons in Prey" page. Weapons don't have to have the same statistics throughout the entire game since they can be upgraded. It's possible thanks to Weapon Upgrade Kits. Every such kit allows you to enhance one parameter of any weapon (you have to find the weapon in the inventory and select the upgrade option from the drop-down menu).
When upgrading weapons, choose the most useful ones first (at the beginning of the game, these are the Shotgun and GLOO Cannon). Moreover, unlock upgrades that influence battle performance the most. For example, for the Shotgun, it's best to invest in developing the firepower, which will make it easier to kill Phantoms. In the case of the GLOO Cannon, it's a good idea to increase its range and glue effectiveness.