Ask your architect to show you visuals of what the house will be like, I guarantee you you can’t read plans like we can. They don’t need to be hyper expensive realtime ray traced renderings, if your architect works in 3D you can sit with them a look at the computer model we work with day to day, that’s enough to understand what it will be like.
Designing a house with an absolutely fixed budget is only possible if you are building a new build house on a flat serviced site and you give a minimal brief and don’t change it after the outline design and you allow a contingency. This practically never happens. After giving you a lowball hard limit on how much they have to spend I draw them a small house and pretty much all clients like to make their houses bigger as the project progresses. I always warn clients that they are going over budget because of extra floor area and I warn them not to get bamboozled into choosing insanely expensive kitchens and finishes by salespeople, but it still happens on most projects. Don’t make last minute design changes, someone will make a mistake and it will cause a cascade of changes that will cost you more or compromise the design. Don’t base your idea of what a decent budget in $/sqft is on what your neighbour self built 15 years ago, or what someone on a TV program about building houses said; the neighbour typically omits lots of costs when telling them how much their build cost e.g. groundworks, services connections, etc. Likewise the budgets people say on TV are usually absolute bullshit. Also remember that your architect doesn’t have total control over the price; what you get quoted by the contractor is what they think the market will bear and this can change considerably over the course of the 6-12 months it will take to get your permissions and finalise the detailed design.