I bought bitcoins on Coinbase (verified my identity and everything). I then sent some coins to a blender service. I waited one day, then withdrew the coins back to my Coinbase account. The plan is now to make a purchase on a marketplace by sending the bitcoins directly from my Coinbase account to the vendor. Is this the correct way of doing things? Or am I supposed to pay the vendor directly from my blender account?
NO do not do that! Every time your bitcoins got to your coinbase account they are linked to you again. You just untumbled your coins basically. You should send bitcoins like this coinbase->Tumber(Helix)->market. That is the fastest way and works.
The best way is to get an electrum wallat running on your computer and do Coinbase->tumbler->electrum->market.
edit: I just said Helix because I run Helix but you can use any of the tumblers on the sidebar.