Congratulations. I've been on HRT for just over 4 weeks and can tell you you'll feel much better for it, assuming it's right for you.
My process was slightly different from yours. I just told my doctor I wanted hormones and was referred to an endocrinologist. He gave me the prescription and a blood test requisition, which I took to a lab across the street from the hospital where his office is. I then went to my pharmacy to get my magic pills and started on them as soon as I got home. Some people here have mentioned they were hesitant to take that first pill, but I couldn't take mine soon enough. I'm now always looking forward to the next one.!

After about 3 weeks, I started noticing changes in my breasts. They are definitely growing and a bit firmer. My nipples and areola also seem to be growing. Also, while I can't be certain, I think my testicles have started shrinking.
All in all, you should find the experience enjoyable!