If I get HRAP, is it a good idea to bring my truck down to my first duty station (at Fort Campbell)?

I would drive. It is much more convenient to be able to transport yourself around than rely on others. Being that you are aviation, they are located on the far end of post so getting to the PX is a bit of a hike.

It depends on how far away your truck is from base, because on hrap you should be working 5 days a week. You also have the option for the army to ship it for free.

I'd say drive it to Campbell with some of your belongings