I have been backpacking for years and switched to a hammock before I got in to biking. It was one of the best gear change decisions I ever made. The main reason is it gets you off the ground - you never have to find a clear/smooth place to set up. The downside is you have to have trees at appropriate distances to hang from. For most people/places this will be a non-issue as trees are pretty much everywhere.
My set up is a warbonnet Blackbird, double layer hammock with a Mamajamba tarp that has detachable doors. If I had the gear change to do over again today what I would change is the tarp. I would get the Superfly as the doors are attached. You will appreciate that when the weather goes to pot.
Speaking of the weather going to pot - I have been in everything from tropical storm rains (tropical storm Lee, I was in the Smokey Mountains that weekend) to temps down to around 0-10deg f with a few inches of snow. What I can share with you is that the tarp will let some (not much) moisture through. Both nights we were in the mountains it rained - a lot - and there was mist coming through the tarp. It wasn't enough to get anything "wet", but it was noticeable. For a straight down rain hanging the tarp a bit higher works fine. I prefer this set up because it allows easier access in and out. If there is much wind you want to drop the tarp down. In the snow I set the hammock up normally, maybe a bit lower, then dig out the snow underneath and pile it against the bottom edges of the tarp. Then I put some snow on the outside along the edges of the tarp. This helps to seal out wind. It still vents through the flaps in the doors. I slept very comfortably this way. I had a thermometer inside and it was around 40deg at my hammock ridge line, with temps under 10 outside.
For any weather, even summer time, you need bottom insulation. I started out with a sleeping pad - therm a rest trail lite, and if it was cooler I put a blue closed cell foam pad under the therm a rest. This was a conversion over from my ground dwelling days. It worked, somewhat, but trying to stay on pads curled up in a hammock is not ideal. The better route is to hang a quilt underneath. I invested in a Hammock Gear down quilt - 20deg model with the highest down over-stuffing they offer. It was the most expensive piece of gear I have bought, but it is convenient and it just flat out WORKS. With winter camping in my adventures having the right piece of gear made a huge difference in comfort and I'm glad I made the purchase. For warmer weather you can get by with less, but you need something. Hanging the insulation underneath the hammock helps because it keeps the insulation lofted, not compressed underneath you. When lofted it retains higher insulation properties. In warm weather a layer of fleece may work, or a blanket hung underneath, but you can dig in to the options. This is a whole science in and of itself.
Sleeping bags can work inside hammocks. However, there is no insulation from them below - you are compressing the bottom. If you turn a lot at night you may find you tie yourself in a knot. So, you may look to use just a blanket or quilt on top. With good insulation below you won't need much on top - and you can use the top to regulate your temp. I use a sleeping bag most of the time and make it work pretty well.
As others have posted - check out hammockforums. Its a great place.