Break it up into two parts:
But freedom is simply the fact that this choice is always unconditioned
I think this quote can be understood in light of something that Robert Barron (who I believe quotes someone else, but I forget whom) often says: one view of freedom is that it is hovering between the "Yes" and the "No." He contrasts this with a traditional Christian view of freedom, where freedom is freedom to do something particular.
Sartre seems to be disputing this - freedom to Sartre is the ability to make any choice one wishes without being externally compelled or influenced.
We shall never apprehend ourselves except as a choice in the making
Again, Robert Barron has a post about this where he sums it up as "existence (unfettered freedom) precedes essence (who or what a person becomes)". In other words, we first exist as something, and through the choices we make are core is defined. This is again in contrast to religious views, for example, about humans being made in God's image (and so our essence precedes our existence).