It will be totally sung. There will be some quiet parts, but the principal parts of the Mass–the Ordinary and the Proper, as well as the readings–will be sung.
In the United States “High Mass” usually means a sung Mass with one priest and several altar boys. In other countries, “High Mass” often refers to what, in the US, we call a Solemn Mass.
“Solemn Mass” in the United States is the same thing as a High Mass, but in addition to the priest there is a deacon and a subdeacon present. The subdeacon sings the Epistle. The deacon sings the Gospel. These latter two also have some additional duties. Furthermore, this type of Mass is sometimes called a “Solemn High Mass,” which complicates things a bit.
There are also the Pontifical Masses, in which a bishop is the celebrant.
I’m about 85% sure your parish will have the first of these three, a sung Mass with a priest. If there is an online brochure or something and you post a link, we might be able to confirm this.
As far as what has changed between the 1960s and now regarding this form of Mass, hardly anything. Some slight details and kinks have been changed, but the overwhelming majority (upwards of 99.9%) of the Mass will be just as you remember it.
This is a High Mass:
youtube.com/watch?v=c32brXXx5k8 (The organ is a bit awful in my opinion, but the singing, the participatory singing, is very good.)
This is a Solemn Mass:
youtube.com/watch?v=TVnvwESokoo