Wafer-scale, high-quality graphene growth, functionalization, and transfer to arbitrary surfaces are required to make the next generation of novel carbon-based nanoelectronics. To that end, we perform chemical vapor deposition of graphene on Cu and find that the Cu surface crystallography affects the graphene growth. Hexagonal, low-index Cu(111) gives high-quality, monolayer graphene at the fastest growth rate. High-index surfaces and Cu(100) give more multilayer, defective graphene. For fluorinated graphene, fluorine chemisorbs to graphene on high-index Cu facets before low-index surfaces, promoting tunable fluorine coverage and graphene bandgaps based on the Cu surface crystallography. Using atomic force microscopy, we confirm clean transfer of these graphene layers to arbitrary substrates with a poly(bisphenol A carbonate) support. Our improved graphene growth, functionalization, and transfer procedures enable the nanofabrication of layered graphene structures.