Moisture and sunscreen are your friends.
Here's a bare-minimum beauty routine for you:
Wash your face first thing in the morning with lukewarm water, with a gentle facial cleanser (like Cetaphil Gentle Skin Cleaner), using just your fingers, and never tug the skin around your eyes. After rinsing, shave if necessary -- though make sure to leave two or three days growth if you're getting electrolysis -- using shaving cream, and a razor that's no more than a week old; always shave in the direction the hair grows to avoid razor burn. Then, apply a toner over your whole face (even a mild one like Dickinson's Witch Hazel) -- this helps to close up your pores, making skin appear smoother. Finish with a moisturizer like Neutrogena or Aveeno that has at least an SPF of 15, and 30 in the summer time. All these quality products are easily found at the drug store. (If you need help finding them, and you're not passing yet, you can tell an employee that your girlfriend gave you a list if you're at all embarrassed about it.)
Shower with a moisturizing body wash. I like Dove's "Deep Moisture," I apply a dab to a nylon shower ball and it lathers much better than with a washcloth. Do your whole body, except for your face. After drying off, use some kind of lotion, again all over your body, to preserve your skin's moisture. This makes it soft and pliable.
For your hair, shampoo and conditioner, at least every other day -- maybe try Suave Keratin Infused shampoo and conditioner, which is pretty gentle and very inexpensive. Use only a wide-toothed comb for your hair when it's wet, as anything else can lead to breakage. If you can avoid using heat on your hair, all the better (though you can get away with this if you have thick locks). Only brush your hair when it's dry. Whenever combing or brushing your hair, always start at the ends and slowly work your way up the hair shaft to your scalp.
Before bedtime, wash your face, as before. But this time use a moisturizer without SPF.
As to your other issues, yeah, don't cut your own hair, go to a hair stylist every two to three months, just to get your ends trimmed, as you'll want to grow out your hair as much as possible. Also, get a pedicure. It's very nice, and then you can attend to caring for your feet on your own once the initial overhaul has been attended to. For all nail care, I like Revlon clippers, they seem to stay sharp forever.
You should notice improvement in the quality of your skin and hair within a month, and even more so after getting onto HRT.