First off, a good overall fitness program that blends strength and endurance that you're comfortable with should be a basis for your own overall fitness. Firefighting involves a LOT of bending, climbing, pulling, crawling, and lifting. It also requires a LOT of endurance. You can be the biggest beast of a person but if you have no endurance, you won't last long. Conversely if you have a ton of endurance but no strength, you're just not literally going to be able to muscle things around like you need to, even though you can outlast everyone else around you.
Find out what the specific requirements of the department's PAT is and train for that. For many years, the City of Sacramento used its own in-house PAT. Now they're using the CPAT. Don't assume that once you've completed the PAT that you'll never have to do it again. Once upon a time I did the Sacramento City Fire PAT back when they ran their own. Relatively speaking, I had no upper body strength, but tons of leg strength. There were portions of the PAT that I just blasted through and some that I struggled with. I never passed... but that's because I focused on the wrong areas of strength development.