Ive never actually confirmed this, but cis girl friends of mine always told me to get the razors "for men" because theyre supposed to work better (and because of pink-tax they're often cheaper :3)

For wet body shaves, i would recommend starting with one that has many blades and then later switching to a double edged safety razor when you've got the flow down. I also recommend getting some body shaving gel for women. Dont use to much pressure and go over the places you shaved with cold water, it's supposed to close the pores. Ive had issues with ingrown hair before HRT so i got myself a ladyshaver, mine is from Phillips. If you don't get grossed out by it, you can buy them used for a lot cheaper. I also got a cleanser with salicylic acid from cera ve and have been using that for the last 1½ years. Works well for me :) Remember to use moisturizer after shaving, your skin will thank you.

I shave my face with a gilette fusion razor because it's worked better than any other method for me in the past, but the blades are crazy expensive. I recommend using a moisturizer instead of an after shave (iirc the alcohol dries your skin).

Edit: Important thing to avoid razor burn: try to remember your hair growth pattern. For me the hairs on my Thighs grow sideways and not shaving sideways there caused a lot of razor burn.