Early on in your final year of medical school, you will have to apply to programs using the ERAS service. ERAS is to residency applications as AMCAS is to medical school applications.
Which programs are good? Well, it depends on what criteria you're talking about. Do you want to be an expert diagnostician or an academic researcher? Some programs do an excellent job in one or the other. Few programs do a good job in both. So it depends. Also, do you want to focus on AP, CP, or both AP/CP?
If you're interested in diagnostics (i.e., surg path & AP), you would get the best training at Mass General and Hopkins. No program compares to these two places when it comes down to clinical training.
If you're interested in academics and research, I would put the Brigham at the top of the list...no doubt about it. Other programs that have a heavy research bias are UCSF, Stanford, UPenn, WashU, and UWash (sure, I might have forgotten a few but these are the programs that foremost come to mind). There's a reason why the academic pathology researcher career track is referred to as the "Brigham model." A fair share of academic pathology department chairmen have trained at the Brigham. Abul Abbas is at UCSF. Stephen Galli is at Stanford. Jonathan Braun is at UCLA. Michael Gimbrone at Brigham. etc etc.
Abul Abbas, I believe, is trying to convert UCSF into the next Brigham. Many highly qualified MD/PhD candidates who applied this year to pathology ended up there. UCSF also has this Molecular Medicine Training Program which will fund up to 3 years of fellowship/postdoc after you complete your residency.
Although I would not put UCLA amongst the ranks of Penn, Brigham, and UCSF, I should mention that UCLA has a program called the STAR program. Although I did not get the impression that UCLA is following in the footsteps of UCSF, the STAR program could attract aspiring physician-scientists. The STAR program is modeled after the PSTP program at WashU. But I don't know what PSTP entails since that program is for internal medicine residents at WashU and I didn't apply to internal med. Anyways, I was told by quite a few people at UCLA, during my interview visit, that the STAR program is more useful for those rare folks who want to do PhD training during residency (i.e., they did straight MD prior to residency). So the STAR program applies very little to the MD/PhD person.
You brought up Mayo Clinic Pathology. Yes, they do have a "physician-scientist" track but I didn't interview there so I'm not well versed as to what makes that track so special. Their pathology program is better geared for training fellows rather than residents though--for example, frozen section call is done by the fellows and not the residents (personal communication). And they do things "differently" in that they make initial diagnoses all based on frozen sections. Some people argue that learning pathology this way might not prepare you for how things are really done everywhere else in the country. On the other hand, I'm sure that you see some great cases, especially consult cases from all across the world...it's frickin' Mayo for crying out loud!
Anyways, whichever way various programs want to structure things (nothing vs. STAR vs. MMTP vs. etc), you will likely do the following if you decide to pursue pathology and research. You're gonna have to do the minimum residency (AP only or CP only) or you can do the full AP/CP. That's up to you. But then you need to find a fellowship/postdoc. The research-heavy residency programs will have the department fund your first year, at least. Then you will apply for KO8 grants after you have generated preliminary data. And lemme tell you, there are quite a few untalented MD researchers, with negligible track records, out there who easily secure these grants and go on to publish nothing and then go back to running their clinics full time. So I don't foresee problems for you to secure a K08 grant. Hence, I don't see why it's such a big deal to have some fancy program that will automatically fund you for 2, 3, or more years for your postdoc. If you're serious about becoming a scientist, you're gonna be applying to grants anyway. And when you get those grants, your pay will be derived from those grants that you've secured.
Do having specific interests and publications help in making you more competitive? Short answer...most definitely! A strong research background will put you in a different tier in the applicant pool. Pathology is not very competitive to begin with and your background will help ensure that you match at your top choice.
You don't HAVE to go into pathology either. For you, I would also consider doing a short-track internal medicine residency. That was my initial plan, actually, but I realized a few weeks into that rotation that I hated it and plus, I bombed that rotation.