Definitely do the sheet cake with buttercream. Since a sheet cake won’t be torted (will it?) you want as much icing as possible. The fondant is mainly for looks anyway and if cost is an issue, definitely save your time on the sheet cake.
Funfetti’s idea about doing a tier out of styrofoam may be a good idea, depending on the budget, but make sure you factor in your time and energy – it still has to be decorated so don’t throw it in for free! I’ve never done one personally but from what I’ve read a dummy costs almost as much as real cake in most cases.
If she wants a large display but there’s no budget for a large cake, how about doing a nice cupcake display with a fondant cutting cake on top? Just a thought!