Ordering
If you order before Shabbat, even if you know it will come on Shabbat, it is permitted. You did not tell the driver "come on Shabbat," the company decides.
It is Amira De-Amira - you tell Amazon, Amazon tells the driver. If you can add a note "please don't deliver on Shabbat" - it is better.
Using it on Shabbat - Techum & Car
The package comes from outside the Techum and by car. Still permitted to use on Shabbat.
Why: The driver works for Amazon, not for you. He delivers to hundreds of people, Jews and non-Jews, this is his job. He does not do it specially for you, and you have no interest it comes specifically on Shabbat.
Therefore it is not considered that a non-Jew did work for you on Shabbat. It is like mail. [Shulchan Aruch 515:9, Mishna Berura 68; Shemirat Shabbat 31:24; Da'at Torah 325:8, 515:9].
Bringing inside - Kinyan
No problem of buying on Shabbat. When you paid online by credit card, you already acquired it (Kinyan Situmta / Dina DeMalchuta). So lifting it from the porch is not a new Kinyan.
Conclusion
You may order before Shabbat, and if it arrives on Shabbat you may bring it inside and use it on Shabbat, provided it is not Muktzeh and you open it without tearing.
NOTE: A longer Hebrew version of this question is available below