My first purchase, pantyhose with a small basket full of unwanted groceries.
My first try on: I had asked a saleslady in the store about some specific women's clothes. Then I asked, do you allow men to try them on? She said, "Oh, yes, come on." She set me up with a room and she and another SA brought me other things to try on.
I have shopped in Walmart as a man and taken clothes into the dressing room. These days, their security is better. The clerk will ask to see what you are taking in. Also, Walmart and many other stores have cameras behind the mirrors in the dressing rooms.
Thrift stores have unattended dressing rooms. But, the clothes are cast off items. I no longer find anything that I want there.
Clothing shops like Cato and Dressbarn are pricey, but they have nicer clothes. The clerks are normally trained and very understanding. They will bring other outfits to the dressing room.
Big department stores train their employees about crossdressers, I think.
Consignment shops are good. Those are clothes that are good enough for the owner to try to get something for them.
My best experience has been to buy something that I like and then pay to have it modified to fit MY body. But, then you have to out yourself to a seamstress...
One particularly fun memory: In a consignment shop, I was holding a dress that I wanted to try on. Someone was in the only dressing room. I was browsing the racks. The owner, a stranger to me, walked past me and whispered to me as she passed, "You can try that on if you would like."