Planning a lesson with faculty members for Graduate School (Advice needed)

Hey guys, this is my first ever post on this forum so here goes.
I am B from Singapore. This August, I will be commencing my studies in Undergraduate Voice at the Yong Siew Toh Conservatory of Music, National University of Singapore.
Right now, I’m pretty open to a path in art Song or opera but I understand the importance of planning ahead in the long run, especially when it comes to Postgraduate education. I definitely would be interested in pursuing my Masters in Music in the USA, but at the same time, it’s not a “do or die” situation, since I haven’t even started on my degree. If it happens, it happens. If it doesn’t, it doesn’t but that’s not to say that I wouldn’t put in the graft to work for it. This brings me to the question I have regarding Masters application.
I have heard that finding a right teacher that suits the student is paramount in ensuring his or her success. I’ll definitely be scheduling visits to the graduates schools of my choice and scheduling lessons with faculty members. The question is, when in my undergraduate life should I do it? I have the option of embarking on an exchange program in either my 2nd or 3rd year in YST and I was thinking about visiting these campuses and schools during my downtime (should my exchange program be in the USA) and meeting the faculty members then. I just have no idea when I should schedule these visits. Would appreciate it if I could get everyone’s two cents regarding this.

You can visit while you are in the US on the exchange program, or in the last year of school. (Obviously if in your 2nd year of a 4 year undergrad program, teachers will hear you at an early stage, but you would have a chance to see if you like working with any of them.) You might also do summer programs, if funding isn’t a problem.