I was on Finasteride for several years for prostate reasons before I started seeing a therapist. Finasteride will block the conversion of Testosterone to Dihydrotestosterone which is much more powerful androgen than Testosterone alone. Finasteride has many effects too numerous to list here, but the main therapeutic uses are prostate reduction in BPH and slowing hair loss in male pattern baldness. We take Finasteride to block the damage of Testosterone to our personal appearance. There are side effects. The most notorious is gynecomastia. This is what we want. About 1% of males who take Finasteride experience some degree of breast enlargement. I am one of those people. That said, if you really want to transition, you need an anti-androgen like Spironolactone to block any other production of Testosterone. Please note that Testosterone is also produced in the Adrenal Glands as well as the Testes.
To answer your questions directly, you will see no rapid, dramatic changes right away. It will take a year or two of just Finasteride alone before you see thinning of body hair and restoration of scalp hair. You could be like me and the other 1% of Finasteride users who have developed a small amount of breast growth after a more than a year of daily use at the BPH doses, which is much higher than the doses for male pattern baldness.
If you are serious about transitioning, then consider laser hair removal and electrolysis. It takes a long time and I wish I had started earlier in my transition. Also, you do not need a therapist's recommendation to start body hair removal.
Best wishes and remember; Make a plan, work the plan and don't look back.