I searched "solarium" in photos on Houzz and found great examples of substantial woven/rattan sets with deep cushions that would look amazing in your beautiful room and also be super comfy!

I would put an easel and a drawing desk in there.

Lovely space...light or dark paint you have lots of ways to go.

reminds me of the Sound of Music :)

I would put in a totally circular sofa centering it below the fan as my jumping off point.

I wouldn't splurge on any special furniture until I've lived in the space for a while - it won't be until you get a feel for the heat and light at different times of the day that you'll figure out what works, and what won't.

In the meantime, shunt some patio furniture in there, maybe a desk for your computer, a round dining table, etc. Anything you put in a sunroom is likely to fade or bleach over time, by the way.

You're very lucky - that is one gorgeous big inviting space!

There are no rules here - this room is what you want it to be. I would just keep it lightweight in color and style so as not to block all that beautiful natural light with bulky heavy furniture. Other than that make it your own.

You may find other uses for such a conservatory - wait and see!

wicker wood or white wrought iron all lend them selves to this kind of room and lots of plants...maybe a bird???
its whatever you style or taste is i like beach/tropical but you maybe have very different tastes....check out magazines and pinterest is loaded with ideas.....

Deco - that second pic of the kitchen - amazing!!

sam0705 - looks like a gardener's kitchen, doesn't it?

You are not wrong; comfy and cozy is always better! If you hope to entertain in this space, I will point you toward a circular tufted banquette as a focal point, with additional chairs and side tables toward the edges, and nested planting tables, large vertical plantings spread throughout. If you do not plan to entertain, these areas are wonderful spots to read and create, as Texas hit on above, as well as a place to enjoy a cuppa and ruminate...and grow hothouse plants, of course. Let proposed activities guide your furniture choices and sub divisions. Beautiful space.

it really is idyllic..i'm so happy for you!! I agree comfy and cozy and lots of plants!! you could grow tomatoes in winter!! BLT's in January? oh heaven! :) and somewhere in your comfy cozy conservatory you must must have a game of Clue :) under a seat or on a shelf!!