I have stopped photographing weddings years ago. I´m doing weddingfilms instead. Doing this and attending friends weddings, I have seen a big change in the industry lately. Many (wedding) photographers here in Europe don´t seem to use flash these days, especially not for the outdoor shots. But even indoors many don´t. They do a lot of post processing though. I must admit I like that style.
Just recently the daughter of a friend asked us to photograph her wedding, and they wanted exactly that dreamy, somewhat overexposed look. I couldn´t talk her into a video instead, so we did an (almost) flashless wedding, and they loved it. So did we, because it was an amazing thing to not have to carry around and setup flash units. Interestingly these flashless photographers that like to call themselves "fine art photographers" seem to charge more than others.
So much for flash. It is good to have, but not a necessity to use.
In regard to full frame or crop sensor: that again depends on the style you´d like to achieve: if you like to have as shallow depth as possible, you´d need to go with a bigger sensor. If you´d stop down your lens anyway you could easily go with the smaller sensor because ISO and noise is not so much an issue for clients than it is for us photographers.
However, it feels weird to show up on a big wedding with an a6300. But if you are confident enough and deliver the results the people expect there is nothing wrong with it, because in the end it is the photographer that creates the images, not the camera.
Regarding Lenses: take a look at Sigmas Art Series lenses - they are nothing short but awesome. I´ve bought the 135mm f1.8 and had my hands on the 35mm f1.4. Not only are they cheaper than (I can only talk for Canon and Sony) lenses, some of them are even better!
EDIT: regarding Sigma - focus wise that´s only valid in regard Canon, I finally bought the Sony 35mm f1.4 for my Sony cameras because the focus with the Canon mount Sigma was too slow. However, the image quality and look was much better with the half priced Sigma.