The blood is for pregnancy if you are a woman or person with a uterus, and also for your blood type so they can put it on your dog tags and ID card.
The vaccines will depend on your vaccination record. If you show up with everything up to date, you might get 1 or 2 more (like meningococcal which is not common for civilians, or Hep A which many do not get unless they travel). You will likely be offered a flu shot (given the close quarters and living with 59 new people, highly recommended, but ultimately your choice). Likely also will offer you Gardasil, depending on your age.
Most PT is calisthenics based, and cardio forward. Cardio is way and cheap to do for PT, no equipment required. Same with calisthenics circuits (pushups, sit ups, BW squats, etc). You may go to the weight room for a few intro classes, but you won't be doing any traditional weight lifting while at BMQ.
