I don't think you have many options without reconfiguring the kitchen, because the worktop cuts across the entrance to the orangery. However the room sizes are great.
I think I'd just be conventional. Small kitchen table for 4 up against the kitchen wall. Big reception room as a lounge diner, hard flooring with an enormous rug in the living room area. Orangery a playroom or second living area with sofa(s). Some comfy but fairly light lounge chairs (Eg tub chairs or John Lewis Arlo chairs), or storage cubes, that could be move around to create extra seating in either lounge area when you have guests.
We have a kitchen table and a dining table and it works well with older children. We eat in the kitchen and the dining table is always free for homework, games, projects etc. You'd just need to ensure you can easily get past the dining table, so choose a narrow one and minimise storage in the dining area.
Another option might be to see if you can reconfigure the kitchen using existing units and worktops, and knock through into the orangery, but I can't see that working unless you lost one of the other doors.