Noob confused about ROM's

I have a HTC Incredible running 2.2, and i understand you need to Root first before anything else, got that, but now I am confused about the ROM thing. I would like to Root to uninstall the default HTC apps that keep causing my 'Low Memory Errors'. If i install Gingerbread, is that a ROM like CM7 is? Confused as to what exactly to do after a root, can i install Gingerbread without rooting? If i want to install HTC sense, is that a ROM?? Thanks for the clarification here, i've searched numerous forums, but can't seem to find specific answers.