>>1287857>Is any old parachute hammock good to camp inYou can get away with it, I slept in an off-brand ~9ft open hammock for years before I got my first proper camping hammock, but I wouldn't recommend it. Most of them are overpriced (here's looking at you, ENO / Grand Trunk) and pretty low quality, not to mention less comfortable. Get yourself a Dutchware netless or the netless from Warbonnet. If you're up to spend a little extra, getting one with a net (chameleon / WB XLC / DH Sparrow) would last you years.
>What underquilt should I go withThat's up to you, but don't cheap out on it. Any of the cottage vendors will do you great - I have a HammockGear 10F Incubator, others to check out are Jacks R Better, UnderGround Quilts (UGQ), Loco Libre... You really can't go wrong with any of those.
>do I need both an underquilt and a sleeping bag?Yes, you will need both if you're sleeping below 50F in my opinion. Most hammock campers get a top quilt (same cottage vendors) to save space, weight, and cut out the uneeded bottom side.
>Who makes the best tarps?I think Warbonnet has the best tarps around, they've got a great range with the Mambajama to the Superfly and the other new "---"fly tarps. I used to have a Hennesy asym backpacker, but since I switch the the Superfly I'll never get anything else.
I should point out, when it comes to tarps there is a HUGE step up you can take when you switch from a silpoly/nylon to Cuben fiber. The price jump is rough but cuben fiber is incredibly light weight, and looks pretty cool too - HammockGear has dope cuben tarps but anticipate spending $300-500 on one.