I took a Grand Trunk Ultralight hammock, removed the stock suspension and inserted Wild Country Nitro carabiners, giving me a larger version of the Grand Trunk Nano 7 hammock. I got the GT UL on sale for $15 at Campmor– hardly worth it to sew my own at that price. The hammock body is just 9oz and the carabiners are 1.2oz each, so my basic hammock body is 11.4oz.
For whoopie slings, I bought 1/8" Amsteel Blue from Redden Marine. I find the 1/8" is easier to work with and it has a 2500 pound rating. IMHO, the weight and cost difference between the 7/64" and 1/8" is negligible for the lengths used in hammock slings.
For tree straps, I bought 8'x1" polyester straps from Arrowhead Equipment. Arrowhead has whoopie slings too.
I use Camp Nano carabiners to attach the whoopie slings to the tree straps.
FYI, all the carabiners can be replaced by simply using a lark's heed with the fixed end of the whoopie sling through the end channel of the hammock and using a toggle with a marlin spike hitch at the tree sling end. You can make a toggle from just about any material as the knot takes the majority of the stress. A dowel or aluminum tubing will do. Some people just use a found stick. I have to concede that is the lightest and lest expensive way to go. The carabiners add some convenience and I think they are easier in the hammock fabric, but the difference is small.
Consider using a structural ridge line to help shape your hammock pitch, a place to hang things and hold up a bug screen. I made one from Dynaglide line, set up like a whoopie sling that hooks into my end carabiners. It weighs 0.4oz. Some folk use Dynaglide for suspension, but I think it is too light with the 1000 pound rating. I *could* use it for a backup sling if needed. It is a pain to splice compared to the Amsteel Blue. It makes fantastic guy lines. I got a batch from Treestuff.com.
I think tarps in the 10×12 range are most effective, but you can go smaller. Diamond pitches allow some very small tarps, but long a-frame pitches give more end protection. Fabrics have all the same issues as ground camping.
For bug screens, some make integrated zippered screens; others make a big zippered bag with openings for the suspension. On the lighter side, some make a "sock" with gathered ends– I'm looking at a DIY project there.
You will need bottom insulation of some sort. Insulation is the probably the heaviest, bulkiest and most expensive part of hammock gear. I tried 20" sleeping pads of several types. 20" isn't wide enough for hips-to-shoulders coverage. Most the pads buckle and really detract from the smooth comfort of laying in hammock. I found a Coleman 24"x72"x5/8" convoluted CCF pad that works. It is just 12.5oz, and I trimmed the corners so it is just 11.5oz. It is bulky– about 8" diameter when rolled. Foam pads are hard to move and manipulate and it takes some wiggling to get it right, but it is an option. You can buy one for $20 plus shipping.
It looks like underquilts are the warmest method for bottom insulation. The are made in full or partial coverage and with synthetic or down fill. They add weight, bulk, and cost to the setup. I think they are a #1 DIY target for hammock use. You can easily double or triple the cost of a commercial hammock system when buying under quilts.
One alternative I have been dancing around it to use a custom silnylon poncho rigged as an under cover and using insulation inside the cover. This is a system call the Garlington Insulator (see http://www.garlington.biz/Ray/HammockInsulator/Insulator.htm) using a light under cover and filled with insulating pads made from plastic garbage bags stuffed with space blankets. I took it one up and made my own insulator bags by using space blanket and double stick tape. One or more space blankets are crumple for loft, folded and slipped inside the bag. You can easily achieve 2" loft, and cheap space blankets are 1.6oz each, so a pad with six layers total weighs 5oz and cost about $6. One pad is 48"x54" giving decent summer coverage. Adding a single space blanket spread full length helps extend the coverage and prevent cold spots.
But I think the real answer for a DIY hammock is to make one like this:
*Make a conventional gathered-end-channel hammock– 60"x108" or longer. The side hems are simple rolled hems. The end channels are 1/2" or so and have triple lines of stitching for strength and safety. Breathability is a plus and DWR is not needed.
*Sew a loose panel on the bottom side– one that will be about 4" deep, so you have a double-layered hammock with a differential cut– roughly boat shaped to match the shape of the gathered hammock and about 7' long. Care needs to be made to have enough room to cover the user's shoulders and feet with insulation on the sides. All the user's weight is carried on the top layer. The bottom layer can be very lightweight nylon with good wind cutting properties and DWR– not unlike a windshirt.
*The bottom layer should have an access zipper about 3' long in the middle of one side and parallel to the length, so you can spread your insulation of choice evenly inside.
*Perpendicular channels should be made in the bottom layer, with 3/32" shock cord drawstrings and toggles– I think 5 channels would be about right. This will allow adjusting the area for insulation inside. This would be done before sewing the bottom panel to the upper one.
*Velcro strips should be sewn to the underside of the top layer to hold insulation pads in place and allow them to hang down, so the fill isn't compressed. They would need to be near the top edge of the hammock, just below where the bottom layer is sewn on and across the ends, just above the user's head and below the feet. Short sections would be fine, saving the weight and expense of full strips. They would be more flexible too.
*Insulation could be quilted down or synthetic fill pads, or folded space blankets, or a combination of the two if a vapor barrier is needed. The bottom drawstrings would adjust the space to suit the loft of the insulation, or in the case of the space blankets, actually carry the weight and move them close the top layer. Insultex pads are an option as well. With synthetic pads, it may be possible to make them with a mesh cover. They only need to be protected for compacting for storage and laundering and they only need to suspend their own weight.
I guesstimate that the main hammock body with the bottom layer, zipper and drawstrings would weigh 20-24oz.
Another option would be to use the pocket system that Clark hammocks use, stuffing them with clothing, folded space blankets, or pillows with down or synthetic fill. The pockets would be sewn directly to the main hammock body and have Velcro closures. You would need 3-4 down each side. I think they would have cold spots compared to the full bottom cover and a lot more sewing. the Clark insulation package is called a Z-liner.
Insect control would be at your option: just a head net for the Spartans, a bug sock (my UL choice), a big bag with a zipper, or an integrated screen sewn to the hammock body with a zipper — all but the head net would need a ridge line.