Your location makes a huge difference in your taxes.
For example, I could never save "thousands" on my taxes. Why? Because my yearly tax bill on my 2400-sf house on a 1-acre lot here in the South is about $1600.
My yearly tax bill on my 45-acre farm in a more rural county is $360. Because we actively farm this land, we have a tax deferment. Another way to get a tax deferment is to have a forestry plan. These things are HARD to get started, but once you've jumped through all the hoops and are "in", it's easy to stay in the program. If I were to sell this land or stop farming /build a business, I'd owe five years of back taxes (ouch). The taxes aren't forgiven ... they're just deferred. Typically you need at least 20-25ish acres to do something like this.
Under this program, you can also get your vehicle's license plate cheaper if it's registered as a "farm vehicle".
If you live in a city, you'll pay city taxes PLUS county taxes. Obviously, living outside the city is cheaper; however, you can't always control that. When I moved into my current house, I was in the county ... a month later, we were incorporated into the city. Drat!
If your city "reevaluates" your property, you can appeal it -- but you need to be ready with evidence that your property hasn't appreciated as much as they say it has.
Pointing out the obvious -- if you build a smaller house, your taxes will be lower. Also, if you have fewer bathrooms, etc., you'll pay less in taxes. Living simple is less expensive than living at the top of your budget.
As for brick vs. stone vs. whatever else, I don't know if that helps /hurts your tax bill -- but brick (and I assume stone) lowers your home owners' insurance because it burns less easily than wood.
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