Hopefully you are in for a very enjoyable journey. As has been mentioned before, each of us experience the changes differently and many of the changes you won't notice until much later and suddenly realize that some feeling or other has been gone for a while.
I can attribute to several emotional and physical changes to the hormones directly while others may have been placebo or just the opportunity to live my life openly and freely. Regardless, I have enjoyed them all.
You asked for a timeline. I can tell of my journey but each is different. I started hrt with both Spiro and E at the same time. Within the first few days I was finding more joy in my life (had to be solid placebo effect). Within the first two or three weeks my skin changed; softer, less oily, entirely different smell, less oily hair. At that point I needed to use lotion once or twice a day because of dry skin (live in a dry climate). Not much else happened until about the three month mark when my breasts became sensitive (actually sore, they hurt!) and my emotions kicked in. In the past fifty years I may have cried two or three times, that third month I probably cried thirty or forty times (real gushers). The ten or so months following added breast development and some fat redistribution, a lot of upper body mass reduction (I could never wear sleeveless dresses before, now I love them). During that same ten month time frame I noticed a change in my relational nature. I had always been a solo loner introvert, now, while still introverted I fully partake in conversations with others, particularly women. I just love sharing life events and emotional connections with the many new friends that have entered my partner's and my life along this path. The only downside is that I have totally lost the ability to put up with mansplaining and idiot guys in power telling me why something won't work......arg!!!! But that is a small price to pay.
Your journey will be different and I hope that you will be able to enjoy it as much as we have. - Anne