If you’re thinking of doing IR at one point, GS > / = Prelim >> TY, not just because you might look better to independent IR residencies (how true this actually ends up being in practice is unclear), but because with the increasing clinical nature of IR, you really want to be as comfortable as possible managing ward patients and ICU patients. The demographic of an IR patient is most commonly the surgical one, but I think any program that has you managing inpatients on the regular to a rigorous extent should prepare you for it. Look at it this way: some IR programs have even gone so far to be the primaries on patients and have wings dedicated to them only. If your patient (since your primary) has a K+ of 2.8 and is starting to feel achy, do you want to have to call medicine every time? What about someone whose blood glucose overnight was 350? Or do you want to demonstrate that you are a clinical specialist, you are capable of taking care of your patients, and you’ll be able to handle it yourself? The more time you spend doing this in the setting most paralleling that of the IR hospitalist, the better. In this case, GS ~= Prelim >> TY, unless the TY is one of those fake ones.
If you know for a fact you don’t want to do IR, or you’re pretty sure you don’t, then TY > Prelim >> GS. Go for as chill a life as possible—there is some contention, but I think the prevailing opinion among most radiologists is that their intern year helped them some, but not that much, and it’s better to not make yourself miserable during it. Bluntly, then, go for the TY that has as little call and night responsibility as possible. There aren’t many left (I’d say 3/4 - 4/5 of TYs aren’t chill anymore, they’re just prelims in disguise), but there are a few chill ones I know, and one or two that are so chill that I’ve heard residents coming out of them actually felt worse for having gone through them.
I think one letter in the “specialty” you’re wanting to do the prelim year in is great, but this isn’t a necessity. They see you’re applying for their prelim year, they know you aren’t going to be an internist / surgeon. That being said, I DID NOT have a letter from IM, and I felt like I got fewer prelim year interview invites than my peers that did. I applied to 47 intern years (way overkill, I know) but only got back like 20 interviews, half of which were TYs, and I only applied to 15 TYs. The lack of a letter may hurt.
The goal number of interviews to shoot for, I’ve heard, is 8-10. Short of that and you start to itch closer to partially matching, and no one wants to SOAP for prelim spots. But if it comes down to this, there’s always surgery prelim programs you can SOAP into because they never fill for malignancy reasons. Worst case scenario is you don’t match prelim, and you fail to SOAP, in which case you have to give up your advanced spot. But again, I think I’ve only ever heard of one case of this, and I believe this was a guy who adamantly refused a surgery prelim year even when the air got very thin.