Hi Ray,
What is the reason you like to slice veggies before meat? Usually for me it’s the other way around, because meat takes longer to cook. Just saves time to do meat first. Plus I like to cut veggies at the last moment before cooking to keep them fresh.
Of course depending on the dish: e.g. I made Roman artichokes a few weeks ago and they needed quite some prep and cooking time so then I started with them.
As for safety, my routine is just based on my typical kitchen routine: keep your counter clean and tidy, think through the steps before you start cooking, buy a big heavy cutting board made from wood, buy good knives and learn how to keep them tip top. That’s it! 
