You can buy land from countries isn't it ?
Sure you can buy land from countries, that's what most people do to build a house. I own land, but if I call it a country and decide to have my own laws on it, don't pay taxes for it anymore and build something on it that isn't approved by the municipality. Than I will pretty soon just lose it, and I don't think any country will sell you land and say "yeah, do what you want with it".
Making an artificial island in international waters would be a better solution.
And the South Pole still has unclaimed territory, so that would also be a solution.
Both require an insane amount of money though.