I am in a time warp on this, as I stopped applying myself to the subject when I got up to owning about ten of the things. The most modern thinking might be different now - it can be solved easily with the DD, or can turn into a vast, and disputable subject adressing subjects of cost, size, lightness, strength, packability, materials and adaptability.
Hillebergs are very good, but not cheap, and that is the one I prefer to use. Had it years; big but lightish and strong. A big one gives good coverage and, pitched low, is very good for camping on the ground
Buy a Hennessey hammock/tarp and you can use the rather good tarp on its own ...
The Australian army ones are very good too ... see if you can find a green one. God knows what made me sell mine, but the auscam is still pretty.
I think Tatonka still make a cotton one, if that is what you might be interested in. I use it as a canopy for the back of the car mainly, but it doesn't leak ever and is better with the fire.
Then there are some uber-light ones made from cuben/dyneema ... try looking at Hyperlite and Mountain Laurel. And many people making very heavy canvas ones. Wynnchester and several others. Weigh a tonne. There are lots of sil-nylon ones too. I have one small one I keep as a kind of emergency annexe, but I had another which just broke, so it went back. For these, you might start by looking at Big Agnes
Have a look at Scarp tents ... just for something to contemplate
There is a lot to be said for the ordinary blue or brown or silvered tarp you pick up at the hardware store. Cheap, very strong, heavy and a little clumsy, but totally waterproof .. if you buy the waterproof ones