How exciting that you are in a position to buy a house at a young age - well done!
My thoughts - and obviously I don't know what budget you have available so these are suggestions that I would do:
As a priority I would remove the toilet from the dining room. You don't want to be hosting a dinner party and have someone pop in there generating smells!
Instead, I would try to get a downstairs toilet under the stairs, taking space from the kitchen if necessary. You only need a small space for a toilet and sink.
I would keep the lounge at the front as a cosy living room, but then at the back remove the inner kitchen walls and have the kitchen-dining room as a big open plan space.
There is a conservatory so presumably a garden. I have a personal dislike of conservatories (but each to their own...) so I would remove the conservatory in favour of having more garden space. And perhaps consider bifold doors from dining room into garden to maximise light.
Upstairs, I would take away the cupboard next to the bathroom to use that as extra bathroom space - this would allow the space needed to add a bath in there. I would not bother with an en-suite if it's just you and a dog.
Upstairs again, presumably the top floor is a loft space rather than a third floor? You could consider adding a window into the roof to get more light into that room.
All of these suggestions turn it into quite a project but even if you have no budget as a first time buyer, it looks livable in on paper.
Good luck with it 👍🏻