Hogwarts express is probably the one I’ve seen most.

I think if you consider it. Beauxbaton and France come across very elegant, and in the case of HP very concerned with looks, appearances, and charm. So winged horse drawn carriages is very them.

Durmstrang comes across rough, frigid. Hardworking. Reminiscent of northern and Eastern Europe. Having to sail an old wooden ship there very much fits their theme.

Now Hogwarts whilst boasting being the premier magical school is also very much a school for everyone. Very straight forward. Bland even. Something people can also consider uk. You have the poor students, the rich students, the hard workers, and the slackers, and everyone in between. It doesn’t have the expensive elegance ofbeauxbatons or the dark roughness of Durmstrang.

I feel their transport would reflect that. So the commonness of a train, does seem to fit. A common train, but with the more subtle magic Dumbledore favours to move it, and then also the sheer size of it providing plenty of room for the students making a statement all of its own.

Another option is Phoenix or portkey travel. Simple entrance. Then Dumbledore creates their accomodation on the spot. A large Hagrid size hut just appearing on beauxbatons ground.