I just noticed something in-game that answers my question.
When you're in the dialogue box at the Equipment Dealer, the color of the background in the weapon thumbnails indicates whether the weapon is compatible with your ship/ID.
The difference is more noticeable if you haven't selected a weapon yet. The background on weapons that you can mount will be black, while the ones that you can't currently mount will have more of a brownish background.
I wanted to be sure and share this here in case a future player is having similar difficulties with finding usable weapons for a new ship.
