Totally up to you what you prefer. I remember I was a bit nervous, so I picked up the key with my parents and went over to my room, moved my stuff in. Then my parents went to the supermarket to get some food while I stayed behind and hid in my room for a while. Haha.
Eventually I was brave enough to leave my room and met up with the girls who were already there in the kitchen (all-girls block, there were 2 third years and one other first year already there). Other girls started to arrive and we helped them move their stuff in, so by the time my parents came back I was a bit more comfortable and happy to wave them off.
We all spent the rest of the day unpacking, we all had our doors propped open and took turns to play music, it was very social. Then the whole block went out the the student union in the evening.