Really nice example. The dial is turning brown from what I can see. As wrote before, the hands are replaced with Luminova ones. I have a similar 145.022-69. The tritium is lovely.
Very nice. As others have said, the hands are superluminova service replacements. If you want to restore the watch to its original condition you could source replacement tritium hands from eBay, but they're not cheap.
My honest but very biased opinion is that this is a very, very nice Speedy! Having inherited from your dad makes it that much more special and it's good to hear that you are going to hang onto it.
I agree on the no rush to service. If it's keeping time and all the chrono functions work as they should you're probably fine for now, although a visual inspection of the movement and gasket would be a good idea. If you plan on making this a daily wear then I'd accelerate the timeline to service.
That watch would make a great avatar photo. Great watch but even better history. The grail, a speedmaster from your dad. Only thing better is a speedmaster from your dad that he got from his dad...