Pack Forest made changes to hunting in 2014, hunting only allowed Friday, Saturday and Sunday. Pack Forest is not a gun free zone, you are still allowed to carry firearms following state laws.
There are both deer and elk there as it is a main travel area between the Nisqually river and areas to the east. Bear also hang around and do their fair share of damage. Because of all the students, hikers, bikers, and horseback riders the animals are pretty jumpy. You can fill actually see fewer bunters on the three days a week than you would in the Elbe Hills area and have as good a chance of filling a tag. Access is easy with roads and trails criss crossing throughout the site. Like said above, park in the main lot, not out near the highway unless you need new glass in your vehicle.
Check out their site, it includes maps of the trails and roads. I spend about 1 day a week hiking it since it is 5 minutes away and almost always see deer, the occasional coyote that messes up getting caught in the open, maybe elk once every month or two and a fair amount of bear sign for the size of the area.
http://www.packforest.org/education/