This may seem obvious, but often people think they have to compromise between function and beauty. They do not. Any architect should be able to design a project that lives comfortable in that slippery neighborhood of "beautiful". It may be that this is hopefully subjective, but many aspects of a kind of architectural aesthetics are not so elusive.
For most folks, the beauty of a building is what it looks like. For most architects it is also what the building is. Part of what makes a building beautiful is that it makes sense - the building is something, not simply an assembly of windows and doors, roofs and foundations. For Modernist architects, the exterior of the building should reflect the uses of the interior - a kind of truthful transparency. For more traditional architects, the exterior facades of the building don't necessarily have anything to do with the interior function, but they should be artfully composed. In all cases, a kind of thoughtfulness comes through. We may not all like a given building, but any well-designed building should be able to be appreciated as such.
Your house should be beautiful. Maybe not cover-of-magazine spectacular, but it should be what architects call "resolved". The proportions of door and window openings should relate to each other, the masses of the building should work together, the trim and casing should reinforce the proportions of the openings. This is not to say that every window or door is the same size. That kind of consistency is boring and frankly lazy. But every house ought to have been on hard enough and long enough to bring the design to a place where the building is something, not a pastiche of different styles or a thoughtless amalgam of parts. None of this is limited by budget. Ever. These things are the basics that every architect should be able to bring to bear on a project. If they can't or aren't for some reason, find another.