Hi Justin,
Welcome to the forum, the 308 is a great alrounder, and I'm sure will do the business on the Hogs, any of the premium 150-180gr rounds will do the job, perhaps the 165gr will be the best comprimise of velocity and knockdown. The best plan is try different brands through the Handi for acuracy, as a well placed bullet is as important as a well made bullet,
Regards Howard.
ps what weight are the Hogs in your patch, here in New Zealand 200lbs is a big one, the tusks length is also imprtant to bragging rights.