I am not from Laminar Research; just a flight simmer from downunder using a windows based system.
From the information provided, your system appears to be OK to run X-Plane 11. Be aware though XP11 is extremely resource hungry generating heat in the CPU and GPU necessitating good cooling. With the use of the 23 inch screen you acknowledge the fact the 13 inch screen will not provide a good image size to view XP.
To run XP you need a dedicated graphics card. An integrated motherboard with a screen connection will not work. What type of card? You should seriously consider using a NVidia card instead of an AMD card for best effect and result.
What model? It depends of what you can afford. I would suggest you have a look at the following link at https://www.youtube.com/user/col2mab/videos from Michael Brown from XForcePC in the USA. Michael builds windows based systems predominantly for X-Plane. His business is recommended by Laminar Research as the only supplier of PCs suitable for XP in the USA. Despite the fact he is a windows person he has produced a number of video comparing video cards between AMD cards and NVidia cards and between models. I further suggest you look/view several of the videos and then decide on the model according to budget.