For my Syrian I use the Ferplast Aladino medium size -
https://www.petsathome.com/shop/en/pets/aladino-carrier - I wouldn’t want to use anything smaller than this. You don’t want anything made of cardboard or anything too small. This is the ideal size in my opinion for a syrian hamster.
In the carrier you can provide a hideaway/house for your hamster to sleep in during the journey. I would add a bit of cucumber to the carrier to aid with hydration and a little bit of food. I would ask whoever you are getting your hamster from for some of her familiar bedding that you can put into the carrier so smell familiar to her.
If you are travelling by car I would advise securing the carrier by putting the seat belt through the handles so it won’t move.
I’ve travelled with my Syrian before for an 2hr journey (although she wasn’t a new hamster) and she slept the whole journey and didn’t seem at all bothered at all but this will depend on your Hamster temperament.
Wish you all the best getting your hamster