My personal preferences with paint medium vary based on my mood, and desire to exprese myself. But a lot of people only think that there are two types, acrylic or oil.
I can make my oils dry as fast or slow as I chose by using different mediums.
Products like Liquin and galkyn speed dying to as fast as acrylics, but the translucent quality is not lost. Linseed oil (among others) will slow drying time. Oils have a glow to them. They flow and blend and move like nothing else. They are the most forgiving of the art mediums and you can easily scrape up you mistakes.
With oils I can make my palette last over a week without putting out new globs of paint so i waste far less. I do this by freezing my pallet in a ziplock when I'm done. I have tubes of some colors that I've had for years without running out even with semi-frequent use.
For my acrylic palettes I will place them on a baking sheet with a towel under them, then I will make sure that the towel stays moist. This will also make a palette that can last over a week.
Safety is a concern for many. And while the information doesn't apply one-to-one for oils and acrylics. Safety should be used when working with either of them. Oils are safe so long as you use odorless thinners, keep am air flew when using potent smelling mediums, keep paint brushes and paint brush handled out of your mouth, and never use thinner to clean hands.
And you can mix the two types of paint when done in the right order.
Acrylic can be used as the under layers for an oil paintings layouts. Never the reverse though. Also never use your acrylic brushes for oils then return them to acrylics. Just use one set for oils and one for acrylics.
To make my life easier i buy cheap latex gloves and use one for my right hand. Its inevitable the brush handles get into paint and then into your hands. Makes clean up a lot easier!