As far as the ground floor is concerned, given that the joists will be supported by the concrete subfloor, then you don't need major timber in there. Id have thought that 3" X 2" timbers would be OK.
As far as the ceiling is concerned, are you lowering the ceiling to give more headroom in the room above, i.e. will the new joists be supporting the bedroom floor? Assuming that they are then 4" x2" should be adequate. If they are only there to fix a plasterboard ceiling to then 3" x 2" should be OK.
Personally, if I were doing the job at my house I would use 4" x 2" timbers again just in case I wanted to use the floor above as storage in the future