If you must make a choice between swerving at speed to avoid an animal and hitting it, the better option (for both you and your passengers) is almost always hitting the animal.
You may have some car damage but you will probably live. And the animals are far more hardy than you can probably imagine.
The trouble with many animal collisions is that the best practice is counter-intuitive as most human fatalities are caused by trying to avoid a collision. Don't try too hard to do that.
DO NOT brake and turn your wheel at the same time.
If the animal is shorter than your hood (eg. raccoon) and you can not safely brake or change lanes, just keep going straight.
If the animal is taller than your hood (eg. moose), and you have room, attempt to smoothly steer towards its rear end and towards the direction the animal came from. It will go forward, so if if you aim at its hind quarters you will miss it. Lift the brake so that the nose of your car is not down and you will decrease the chance that the tall animal comes through your windshield.