What type of doctor is better suited to advise a person without a spleen on a vaccine regimen an immunologist or infectious disease specialist?

Either: Overlap of interest; internist may be of assistance as well.

Either one: Both are capable of giving you the information you're looking for.

Family Physician: Your family physician should be able to advise you on the vaccine guidelines.

Either fine: Id is more easily located, and focuses on the conditions vaccination would be addressing. In general, majority of surgeons / family doctors / internists would be competent in managing a post-splenectomy patient in terms of prophylactic vaccination.