There is nothing rude about saying my tv will be in my room.
As far as buying things together for the apartment, make sure in advance that you know what will happen to the item at the end of the year when you go separate ways. My kids roommates generally had one person buying and owning items and took turns with purchases. Either way you are not REQUIRED by anyone else to share in expenses for an item - but if you don’t share in the cost then don’t share the item.
I don’t have a problem with 1st person choosing the room when she arrives. You can discuss changing at mid year, tho you may decide that it’s not worth the hassle of moving everything.