Ohhh, let me argue this both ways, just so I can be of little use as possible
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Do the TG first and then the TF. Just like in comedy, you should build UP, not down. It's called heightening. As weird as growing a penis would be, at least it's something recognizable. Going from that to some kind of animal is turning the weirdness up.
If you did the beast stuff first then the TG kind of feels like "oh, well that's not a big deal NOW."
Watch 'Ghostbusters' and 'Men in Black' again to see how the main characters are introduced to weirder and weirder things as the story progresses.
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Do the TF first, then the TG. The whole point of TF is about giving in to animalistic instincts and losing control to your body's desires. You want them to experience THAT and be frustrated by their horniness. Then, when that cock appears, there's no logical thought process about it. It's just "finally!" and then right to fucking.
I love a good TG story with real-world ramifications, but you don't want anyone in this story contemplating the gender change in a rational, logical way. That ruins the natural instinct stuff if they're thinking about clothing, bathroom use, or their jobs. If TF is your core, really stay focused on that.
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I'm sure that doesn't help at all. I'm not a fan of TF myself, so maybe I've said something that you regard as "wrong" and maybe that will help you choose!