I Bleed and Bruise Easily, Will This Affect The Outcome Of A Hair Transplant?

If you bleed or bruise easily then you may potentially have more temporary bruising following the hair transplant, but it will not affect the ultimate outcome of the hair transplant.  If you scar badly or keloid this ultimately could cause a problem in the donor area, however this will not affect the ultimate survival of the grafts in the recipient area.   However the scalp is typically an area that heals amazingly well when it comes to scarring compared to other parts of the body.  I have done several hair transplants on patients whose donor scar healed excellent even thought they have bad scars or keloids on other parts of the body.

Would I be better off going with FUE or the strip procedure, or does it even matter?

This answer to this question is complex.  Both types of procedures cause scaring, therefore both ultimately could create an undesirable scar.  The answer to this question would also be affected by the amount of hair transplants the patient will ultimately need—i.e.- the more you need, the more likely I would go with a strip procedure.