I would recommend DO.
I did the Caribbean MD thing. I did not have to. I had good stats including an undergrad GPA of 3.588 on 4.0 scale (I said good stats, not great). My brother is the department chair of a surgical specialty at a major US medical school, president of a medical specialty association, and offered to help me with my application - in retrospect I don't know what I was pridefully thinking - I should have gone this route. Having someone on the inside of a medical school is a huge help for people with only "good" stats such as myself.
If you pick one of four Caribbean schools and make sure you do your rotations in ACGME approved hospitals with a residency program in whatever you are rotating in (ex.do a derm rotation at a hospital that has an ACGME approved derm residency, a fam med rotation in a hospital with a fam med residency) than you are good to go in all states. If you attend other than the big 4 - you possibly won't ever be licensed in NY, California, NM, Tennessee or Indiana (which follow Californias guidelines). If you rotate in facilities not properly ACGME affiliated there are states you cannot apply for licensure : such as Rhode Island and Oklahoma which require every minute of every rotation be done in greenbook ACGME hospitals.
Plus if you go Caribbean you have to complete more residency to get fully licensed. If you go United States MD , in Arizona you can be fully licensed after 1 year of residency. If you go Caribbean MD you must complete all 3 years of residency before you can get licensed in Arizona. You have to be licensed fully to moonlight - which can double your salary as a resident. You can moonlight in urgent care and make $80-100 an hour, versus the $14 you make as a resident. A Caribbean MD can get fully licensed in some states like Iowa and Utah after 2 years though. I am not sure what DO rules are - but I have been told by DO's that there are some states they can just get fully licensed in as DO's immediately after school without any internship or residency.
Few people will ask any MD where he went to school - not a likely question, although it does happen. If you practice in a small town everyone will know. You can always dodge the question a bit by simply saying you completed your training with "____ residency program" or "University" if they administer the residency program. So if you do Caribbean MD and finish residency at a residency program administered by University of Wisconsin,for example, you can always say you completed your medical training with University of Wisconsin if the Caribbean thing bothers you that much. But if it bothers you that much you really should stay stateside.
However some people tend to think that DO's are a bit defensive, and tend to go about constantly trying to prove they are every bit the doctor an MD is. Some percieve DO's with a chip on their shoulders. People won't need to ask if you are an MD or not - they will see the DO after your name.
Its easier for DO's to get into some residencies like emergency than for a Caribbean doctor. And as was mentioned as a DO you can apply to the DO residencies, AND the MD residencies - but a Caribbean MD can only apply to the MD programs. However I have had 2 DO's tell me that they think the MD residencies are better than the DO administered residencies. But in any event, DO's can universally be licensed in all states without any extra hoopla.
I think its easier to graduate with low debt as a Caribbean MD than a United States DO.