You'll need to do some questing to earn the rights to purchase the plots. But the Plots will cost 5000 each. As part of the purchase price the plot will already have an anvil, lumber pile and a chest with enough material to build an unfurnished Small House.
Sawn Logs cost 10 each. You'll need 17 for the Small House/Entryway (included in the price of the plot), 47 for the Main Hall and 14/18/24 (depending on wing choice) for each of the 3 wings. This is the only other cost that is unavoidable.
Stone & Clay can be mined on site for just time & effort. You can also pay your steward to buy them for you, though I can't imagine why you'd want to.
Lastly you'll need Iron & Corundum to make hinges, locks, and iron fittings (for the doors) and lots of nails. Whether you purchase these or mine them yourself is your choice.
All in all 200K G should be more than enough if you don't purchase all of the required materials.
For the purposes of the achievement, no furnishings are required, but, FWIW, this is another case of either handing cash to your steward or gathering/assembling yourself.
Wings with sloped roofs (the 18 log group) only require you to make hardware for 2 doors instead of 3, due to a lack of 2nd story access.
If your "completion" of Skyrim includes a rebuilt Thieves' Guild, then consider visiting Riften for your Ore/Ingot needs. There's a Smith in town and 3 in The Flagon.