I had facial surgery as part of my transition in my early 30s -- and now, approaching 50, I live a woman's life. Facial surgery was profound -- it was the "real" sex-reassignment surgery in my experience.
Of course, there's more to passing than the shape of your face. Beard removal must be a priority -- I'd start immediately, as it usually takes a good couple years to finish. Likewise, HRT usually takes several years to manifest the changes we need for our bodies.
Even more important, though, is voice. It took me six months of practice and training to finally find my voice, and several months after that to strengthen the muscles necessary to permanently lock it in. It is voice, in my opinion, that makes or breaks long-term passing.
In the last two decades, I've been misgendered six times -- all in contexts where I was being seen for the first time, like at the grocery check-out, by people who weren't paying attention to me and only saw a tall person with a somewhat broad-shouldered aspect. In every one of these situations, all it took to reverse the misgendering was to speak -- "Could I get plastic bags, please?" -- and then I'd get apologies and expressions of chagrin, which kind of shows you what people really think about misgendering someone. A great voice can reverse a wrong initial impression.
It's even more crucial for long-term relationships (lovers, friends, colleagues) and all the conversations that will ensue. Which brings up my other point -- there's more to passing than just how you look. After all the body work is done, there's still socialization to pick up on, and that won't fully happen if you're "out" as trans. If passing is your concern, it's not a story to share with the world as you transition. It takes maintaining your narrative privacy -- which typically entails packing your bags and moving to someplace new to start your new life.
Do lose weight -- you'll get better surgical results if you're fit (say a BMI of 22 or so), there are social advantages to being more slender, and it's a lot easier to find clothes that look good, too.