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To answer a question OP, yes you can just use a hammock and tarp for sleeping.
This is what I slept in 2 nights ago. It's about as budget of a setup as you can get that will actually work.
The tarp I use is a UST Base tube tarp 1.0. It can be zipped on the ends a d turned into a simple tent if need be, which is nice in case you need to use it as such. As I use it, it's a large tarp for about $30.
For my hammock, I have a Yukon Double. Any double parachute hammock will work. I'm a fan of Wildhorn Outfitters hammock on Amazon. For $50 you get straps to hang with and a nice 11ft hammock. I personally use ENO atlas straps as suspension. They're about $25 on Amazon and work really well.
In a hammock you do need insulation under you. A simple foam sleeping pad for walmart works. They're about $10. You can get a thermarest like the one another anon posted before. I personally use an underquilt, which is a step up from a pad, and considered the best hammock under insulation. I use a Snugpak underblanket. It's $52 on Amazon and the best underquilt for the price, nothing else is even close to that price and it's actually nice, will be good to about freezing temps, and can be used with a pad to go lower.
For my top insulation I use an unzipped mummy bag laid on top of me. Any decent bag will do. I have a Gander Mtn brand one, called the men's chilkat 20. They go on sale for $50 often, and are actually really nice bags.
Hopefully some of this helps of you decide to go the hammock route. I love sleeping in my hammock.