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The nut broke off and had a small red ring/gasket between these connectors. I'm an noob but can follow instructions. Please give suggestions. Thanks
Below there is a water valve 
which may be used as an alternative if the above (cupper?) pipe is inconvenient to use.
You need to cut off the end of the pipe and get a new fitting there which mounts to the pipe and threads to the wall. Take measurements and photos of stuff and go ask from your local plumber for parts, in here we very rarely use soldered pipes and instead we have compressed fittings which are pretty simple to install (and also pretty easy to fuck up, so maybe look for a youtube-video or something if it's your first time).
Not a lot of slack on that bend, gonna be a bitch and a half working on a new compression fitting and sealing it. Dog speed, OP
You're not wrong on that. Might be easier to get some new pipe and couple of fittings to make whole new line.