love letters
Also, I've come to the conclusion that it really doesn't matter nearly as much as we think or like it to matter. We might think it is a big deal, but really each program interviews about 100 people each year. And many applicants have sent a similar email saying "you're such a great program, i'd love to come here, blah blah blah", so 1/25 (rough minimal estimate) emails saying that means nothing. And the value of such emails decreases when more of the similar emails are sent. And then you take into consideration of all of other emails sent from past years, and you reach the conclusion that letter of interest emails mean diddly squat and might annoy if anything. "You're first" letters saying you're going to rank them first might mean something if the program hasn't been burned by such letters in the past. Again, it might also hurt you. They might think back to a similar candidate like you whom they really liked in the past and told the program they would rank them 1, and then end up not, and now if you say you're going to rank them 1 you might remind them of that person. I think the safe bet is if they reach out to you, then respond back saying you really liked them. If they haven't reached out to you yet, don't initiate.
tl;dr- it doesn't really matter...