Why would someone steal my debit card number, order stuff online and have it shipped to MY house?

The total was less than $300 and the items that I could not cancel before they shipped actually DID arrive at my house. Someone also got hold of one of my credit card numbers and made some very low dollar transactions online (for online services not for item purchases). Now it appears that someone is using my name, e-mail address and cell phone number to try to 1) transfer money wirelessly to China (not from one of my accounts); 2) set up the ability to receive credit card transactions online for a business; 3) get information from the goverment regarding funding for a small business.

I have checked my credit reports and there is nothing adverse on any of them. Needless to say, the debit and credit cards have been cancelled and re-issued with new numbers. I'm thinking I should probably change my cell phone number and notify Yahoo that my e-mail address is being used for fraudulent purposes and hope that they can cancel it - and then I'll start using a different e-mail address (WHAT A PAIN!).

I know I should put a fraud alert on my credit reports and file a report with the local police. What I'm wondering is what this person (or persons) are actually trying to do.

What they are doing specifically is setting up another you. They are recreating your identity so that they can sell it to a foreigner who is probably a terrorist or a criminal. They pay upwards in the thousands for good identities that someone does not report on.
You should report on it. It is through stolen identities that were reported that they have caught a lot of the terrorist acts before they have happened.
They are checking the credit cards to make sure they are active, so they can verify that you are real, now your life is gone and in the hands of some foreigner. They have it sent to your house so that online they can get a receipt printed up that has your address on it.
You really should report this.

Some online sites will only deliver to the credit card billing address. Perhaps the person who stole your credit card number hoped to snag the packages from your house.