There are three types of weapon slots: Light, Heavy, and Missile. The weapon slots are abbreviated as LT, HV, and MS in the in-game 'pedia. Each type of craft weapon can only be equipped in its matching slot type. For example, 25mm cannon is a light weapon, so it can only be equipped with a LT slot. Seagull missile launcher can only be equipped in a MS slot.
It is possible to browse the tech tree of the game either inside the game, or on the wiki website; so you can find out what you need to research to get bigger weapons from that; but my advice is this: just play the game. Don't bother try to bee-line particular tech types, especially on your first playthrough. Just play the game using the information presented to you in the game. If you don't have craft weapons - that's no big deal, it just means you aren't ready to start shooting down ships yet. Just do the best you can with what you've got; and what you've got will increase as you progress through the game. That journey is what the game is about.