Choose results, not speed
Both enchantments are incompatible on one regular pickaxe. Fortune does not increase the tool material level: diamond ore still needs to be mined with an iron pickaxe or better. Reference: Minecraft: ender chest.
Diamond Ore from Fortune III yields 1–4 diamonds, but one diamond remains a possible outcome. ancient debris does not reproduce Fortune. Silk Touch does not allow you to take away the mob generator in Survival.
When to store ore in blocks
Collect suitable ore with Silk, then place it at the base and process Fortune. This allows you to wait for Fortune III and not have to wear multiple types of placers. Experience for such ore is gained at the resource extraction stage; Silk's transfer of experience from the block itself does not give out experience.
Before processing, spread the ore over a solid floor. Name the pickaxes “Resources” and “Blocks”, but read the hint before the vein: the name does not change the enchantment.
For the diamond mine, use a separate layer and path plan: Where to mine diamonds and how to lay out your mine.
Practical uses for Silk Touch
The ender chest with Silk Touch falls out intact. Without it, you get 8 obsidian with a pickaxe and lose the Eye of End, but personal content is available through another ender chest.
For stone, Silk removes the smelting step for cobblestone. For glass, it helps to return the block when rebuilding. Move the bee nest at night, when the bees are inside, with a suitable tool with Silk; the departing inhabitants will not be drawn into the object.
Rules for transferring an occupied nest are given here: Bees, honey and honeycomb: a small apiary.
