Assuming NEW ACOUSTIC grand piano, my guess would be a Pearl River brand grand piano, say about 4'7" in length. Probably less than 6500 USD (this is just a wild guess). The price of maintenance should be the same for all pianos - same price for tuning, same price to maintain a stable indoor humidity level. Basically four tunings the first year, two tunings a year on average thereafter, different technicians charge different rates at different areas, may be around 70 USD per tuning in the US, can be way more, can be way less. Depending on your local climate, you might have to spend a lot to stabalize your piano room's relative humidity level, or your might not need to do anything at all if the outdoor climate is stable year round. May be you need to run a humidifier, may be a dehumidifier, may be both at different times of year. Very hard to say. It also depends on how well you expect your piano to perform.
You can also buy a grand-piano shaped DIGITAL piano. Much cheaper, never needs tuning, immune to humidity swing as well, just need to pay for the electricity to power the thing. But I have no idea which brand/model is the cheapest among the grand-piano shaped digital piano, guessing probably 2000~3000 USD, but this is also just a wild guess.

I am really curious, are you really serious about buying the cheapest possible grand piano? What do you intend to use it for?