What trail_rat said.
If it’s not built already I’d seriously consider a sun room over a conservatory, they can be better insulated in the roof meaning they get the light but keep the heat in when cold and heat out when too hot.
Next best thing is well insulated glass, you honestly want the lowest U value possible as otherwise it’s more of a greenhouse than anything else. My folks have the plastic sheeting for a roof and it’s murder, too hot on sunny days, temperature drops like a stone at night and noisy as hell in the slightest drizzle.
Building a conservatory right is expensive but probably not as expensive as heating or cooling a badly designed one over it’s lifetime. As a concept they are great, as actual real buildings they are crap, ever seen a conservatory in a hot country? There’s a reason for that…