Welcome from Florida.
A cheap starter hammock like you mentioned is a good idea. Use it to attend some group hangs (see trip planning sub-forum). You will learn an awful lot and get to jump in a lot of different rigs. You can also see first hand how different suspensions work.
I think you will eventually like a combination of tree strap and whoopie sling. That system is simple, lightweight and less bulky.
Personally, I like to have separate tarp and rain protection for me. It's advantageous to first put up you tarp, then deploy the hammock in the dry underneath it. With separate rain protection, you can then move around the campsite and stay dry.
"Life is a Project!"