I wouldn't use a plastic shelter. I have never had one but condensation would be a massive problem. I used to keep a 1200 Bandit under a rain cover in the garden over winter. Prior to leaving it, I'd wash it thoroughly and then spray GT85 on everything except brake discs and tyres. Every few weeks I'd uncover and repeat the process as required. That bike made me money when I sold it.
A centre stand is a great buy as suggested above. Just be aware that installation requires removal and refitting of the right hand side end can. That process can be very scary due to the thin metal and corrosion! So be prepared for a “plan B” if things go wrong.
Best of luck!