You're thinking along the right lines, but I definitely would not recommend paracord. Even though it's rated for a tensile strength of over 500 pounds, an average sized person can put more stress on it than that, depending on the geometry of the hang. The tighter the hang (flatter), the more stress on the suspension. It's generally recommended to put enough slack in the line that it hangs at a 30 degree angle. This relieves a lot of strain and is typically more comfortable, depending on the hammock. Plus, paracord is pretty heavy for it's strength and holds water. What most people use who want an ultralight suspension is what's called whoopie slings, and they're usually made from a dyneema cord like Amsteel Blue. You can either order them pre-made, or get the line and make your own. It's really easy to do; just search for how-to videos online. In addition, the wider straps that go around the trees are called tree huggers or tree straps, depending on whether or not they've got loops on both ends or just one. All the little details of how to connect this stuff are a bit much to go into here, but there's ample information online. Hammockforums.net is the place for this kind of stuff. I would also recommend watching the series of beginner videos by Shug Emery. The only thing is, he loves his hardware. That's understandable; it makes hanging more convenient, but adds some expense and a few grams of weight. It's possible to setup a whoopie sling suspension with nothing more than a couple toggles for hardware (or found sticks).

Good luck.