That would depend on your suspension system I guess.
When I firsts stared I used a HH Exped. and tied the HH Fig 8 lash. I quickly started using the Trucker's Hitch with this set-up and licked it even better.
Pretty soon I was building my own hammocks and using the Four-wrap Knot finished off with a Slipped Half Hitch; very simple and very effective. The only problem is when I encountered trees that were so big I could only get a couple of wraps. I then used the Fig 8 Lash or a Slipped Buntline.
I have experimented with several carabiner combinations and didn't really like any of them. Set up was faster with some of them, but overall everything was more complicated. I started using the double rings a few months ago and I have been happy with them so far. The best thing is being able to adjust the hammock under the tarp. It adds some complication to the set-up, and weight, but overall I think I like it. The only knots I use are a Slipped Half Hitch at the rings.
I use Taught-line Hitches on my tarp guyouts, Highwayman Hitch to hang stuff from my suspension ropes or ridgeline, a Bowline for pretty much any loop needed, a Clove Hitch tied to my hiking poles to raise the tarp corners and a Mooring Hitch to tie up the boat!