I tested it on some online purchases and it all worked out.
Step 1: Establish a secure connection using a public wifi network in your city on your Linux Laptop.
Step 2: Use a No-Log VPN together with Tor to access the online store website without attracting the attention of your ISP. If you live in the US, China or the US, you don't want to draw unwanted attention.
Step 3: Use a disposable email and a burner phone number to register on the online store website.
Step 4: Uses various package forwarding services to route product deliveries to a secure address.
Step 5: Pay everything using your anonymous ATM card, or any anonymous VCC with fake names.
They recommend using Tails always, but I'm satisfied with my Linux version.