If you stay on the cheap side, there isn't much gear that is going to be different between using a tent or hammock.
For both a tent and a cheap hammock setup you need a sleeping bag and a pad. For a hammock setup you additionally need a hammock, suspension and a tarp. For a tent setup you would just need a tent, but keep in mind that a tent is heavier, bulkier and most likely more expensive than a hammock and a tarp. You can get a hammock and a tarp for about 20 bucks each on amazon, ebay, or ali.
Either get a mummy shaped sleeping pad or, if you got a folding one, just cut it into the shape of your sleeping bag. Put the pad into the sleeping bag to avoid it slipping away when you sleep. I never bothered with a mosquito net, but you can just cut out a piece from a broken mosquito net and hang it over the ridgeline and your head.
For more information on hammocks I suggest you check out shug and this playlist
https://www.youtube.com/playlist?list=PLqDZ8QEZYSn5vKbUEp4nlS5mN4c8np_ik https://www.youtube.com/user/shugemery Another great resource are the
hammockforums.net (or the
haengemattenform.de if you understand german).