I wasn't seeing the photos before.
The bridge is the same setup as mine, just the bridge with no tailpiece. To install the Gotoh 510FB you need to remove the factory bushings on your guitar, because the Gotoh use a special bushing with a metal bottom in it that after you have set the height with a bigger hex key then you wind a grub screw down with a smaller hex key that locks the bridge rigid against the insert.
There are actually four different hex keys that come with the bridge (see the video) and these adjust a heap of things. There are grub screws fore and aft on the bridge itself, you can use these to adjust gross intonation. Then each saddle has a grub screw; you loosen those and set the intonation, then tighten them down to lock it in. There are big hex keys that adjust the height of the bridge. There are no screw drivers or thumbwheels involved.
By the look of the headstock you want the same tuners that I have fitted to my Schecters, due to the angled leg for the locating screw. The Gotoh part number is SG381 MG-T. You have a wide choice of buttons. The 01 or A01 shape is probably closest to yours, you might want to stick with that given the shape of your headstock. It is a common one though that you can find on eBay or through companies like Philadelphia Luthier Tools & Supplies (they don't keep the 510FB bridge though). On all Gotoh parts there is also a finish code. Mine are Cosmo Black, which is CK. I think Black is B.
So the bridge would be 510FB-B and the tuners would be SG381-01 MGT-B if you were getting the same spec as on my Schecter, but in Black with the buttons more like what you already have (mine are the 20 button code).