From what I've read testosterone increases metabolism, so HRT (for MtFs) can decrease metabolism making it harder to lose weight. I'm not sure if losing weight while on HRT would help with a more feminine shape, but I'm doubtful it would. From personal experience I was slim before starting HRT, and I'm still slim after being on HRT for 5 months, but I'm noticing my body is taking on a more feminine shape. I would just start trying to lose weight now, it shouldn't have any effect on how quickly you get results from HRT.
As to how long it takes for someone to start HRT, it really depends on the person. If you are out to family and friends, live full-time, have legally changed your name, you'd probably get it in one appointment. Of course not many people are that far along before starting HRT, but for my psychologist he said these were the two most important things for him for if he writes a HRT letter for someone:
1. You have a support system, either you have friends that support you, family, maybe a support group. Just having a person/people to go to when you are feeling down, transition is a hard thing to do alone.
2. You've gone out as gender you wish to transition to at least a few times, and see how that makes you feel, etc (going to the mall with a friend, visiting family, going for a walk, just something out of the house).
Once I had that and I still showed interest in starting HRT, my psychologist was more than happy to write my HRT letter. A lot of it depends on your situation though.
I've heard that the guidelines for treating transgender people (The Harry Benjamen thingy) says 3 months of therapy (or something like that), but most therapists just use that as an idea, and take each person as a case by case basis. Anyways hope this helps!
