>>578205Hammock camping can be more involved than tent camping, but that's half the fun.
A rain fly made for hammocks is better, and lighter, but no reason why a tarp won't work. Use that for now. Upgrade later to save weight.
An underquilt is almost a must. Some people don't use them, but below 65 degrees your butt gets cold without one. They also have the advantage of comfort. Getting into a sleeping bag in a hammock is much harder than getting into one on the ground. With an under wuilt, you use a top quilt like a blanket, and it's much less restrictive. I use a sleeping bag as a top quilt, works just fine.
You have options for an underquilt. The cheapest is to make your own out of a poncho liner for about $45. It's called a PLUQ (poncho liner underquilt). Easy to make, and warm. Pic related.
Arrowhead equipment makes one called the Jarbidge. It's 3/4 length, and $100. Much cheaper than most other options. People seem to like them. They have a full length option for like $150.
You can also get by just using a sleeping pad under you. A $10 pad from walmart will get you by just fine under a sleeping bag, but isn't as comfortable in my opinion as an underquilt.