It all depends on the fixture . Do you have a staircase off this entry ? Post pics of the space , the fixture you like and then you will get some ideas .

It all depends on the room, and the fixture. Pictures are the most helpful here.

"Should I go for an 18" or 22" wide lighting fixture?"

Yes.

Add length and width of the foyer...14.5' and convert to inches...14.5" I think you can get away with 18", but no larger. Ceiling height has nothing to do with the size of fixture, but you want the bottom of light at least 7' off the floor.