Carnage.
Here is my routine:
1.) Cut and clean parts.
2.) Wash parts
3.) Prime parts
After that procedure varies a bit due to the different types of models I build.
3A.) Put on surgical gloves for future handling if parts to prevent oil from fingers to get on the Model. Usually used for plastic models and smaller items.
3B.) Put on surgical gloves and insert metal rods into parts to serve as stays and allow me to manipulate them without touching them. Usually used for large pieces, resin & Vinyl kits.
Once the primer is on I try to touch the kit as little as possible with naked flesh.
On large scale Items I tend to put down a layer of top-coat between paint layers, this allows for touch-ups and corrections without affecting the underlying layers.
The oil from your fingers is bad news.