Should I think about insulating a cheap conservatory? if so how do I do it?
For the solid walls you could use insulated plasterboard (example only). This would reduce the dimensions of the room slightly and require new skirting boards and finishing around windows and doors.

I think other thickness of insulation are available.

You're already thinking of replacing the roof, so look into double glazed panels if you can get them to fit.

Secondary double glazing over the windows might be a sensible option too.