The stands are quite handy. You can get by without them, but you need to have the saw screwed down to something or it'll try to jump about. An old black and decker workbench would do.
The 'sliding' mitre saws can cut wider pieces of wood. A compound saw would probably do for what you're doing, but there's a high possibility that one day you'll go to cut a wider piece of wood and wish you'd bought a sliding saw instead
I'd recommend you watch a YouTube tutorial or two on how to use one. I wish I had done that at the start!