Can use either.....I usually inject and rub.....since you aren't looking for a dry mean I would wrap from the start in the oven or use the crockpot. Key is low and slow. 200-225 for 1 hour per pound then use a fork for the pull test....if it pulls apart its done...still tight cook a little longer.
I remove the meat and set the to the side...let the broth cool then place in the freezer for a few minutes...less than an hour....to let cold remove any fat (grease) off the top. While broth is chilling I pull apart the meat and place in the pot or pan. I then pour the broth back over the pulled pork and leave it in the fridge for 4-6 hours. This allows the meat to absorb spices and fluid from the broth. I place the meat in a steamer so that the meat is above the screen and excess fluid can drain below and place in the fridge.
Warm and serve as needed.....
pretty much like I do it. I use a crock pot liner bag, rub meat with favorite spices and pour a can of your favorite soda (Dr. Pepper for my wife, Root Beer for me) and let it cook on low until it pulls easily. Remove meat to a large dish/bowl, pick up liner bag and pour juices into a container & place in fridge (freezer would be faster) to let the grease separate. While juice is chill'n, get two forks and go to town shredding the pork. Skim grease off juices and pour over meat. We usually will add a bit of BBQ sauce (whatever is your favorite).