I had 4 practically new tires put on and now the thing shakes/vibrates until you

Makes one wonder why they had these "practically new" tires on hand to start with, as in they may have already been installed before and this same problem occurred. .... Take the vehicle back and get the tire shop to check it out! ... Inquire about those tires!

In my honest opinion, I know that they only replaced your tires but sometimes they are fairly rough when they are taking them off (kicking, shoving, prying) if they are stuck on. I had THE EXACT issue with a Dodge Intrepid I once owned. Got to looking, and noticed that I could wiggle the whole wheel around just a little bit when I pulled and tugged. Turned out that my tire rod ends had been damaged and driving like this is dangerous. I replaced and solved the issue. Other than that, you may have a balance or slight alignment issue.