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Is X-Plane able to run satisfactory on your laptop? I mention that because the laptop seems to fall short of Laminar’s Recommended hardware requirements.
Anyway, as for the external monitor, you’ll want a monitor large enough and with adequate resolution to be able to see the outside scenery and read the instruments inside. In order to see those objects clearly, to me, a 27-inch 2560x1440 monitor is a minimum (assuming the laptop can display such resolution). A 32-inch would be better.
I am not from Laminar Research; just a flight simmer from down under.
I am of the same opinion of disc that your laptop will not run successfully and the minimum screen size should be in the order of 27 inch. What is not mentioned in the recommended requirements is good cooling in any computer. X-Plane generates a lot of heat that has to be removed.
X-Plane is resource hungry requiring as a minimum a near top of the range CPU and a near top of the range GPU. These two items require the cooling. For best effect go for a NVidia graphics card and an intel CPU. These products will give you best performance over AMD products.
If you do find you need a new system to run X-Plane and you are looking at some decent hardware then consider a purpose built Windows based PC.
Despite X-Plane being developed using a Mac System LR staff recommend a purpose built Windows based system. By going for a purpose built system you can upgrade your individual components as and when you can afford component upgrades whereas an off-the-shelf unit will possibly not give you that flexibility.
Now in relation to your original question, consider using a television screen in the largest size you can afford.A far cheaper option than a large monitor. The screen should be at least 1920 x 1080 format running at 60 Hz (FHD is the starting point although may be difficult to purchase as large screens are now generally UHD)
I am sure the recipient will be pleased with what you plan.
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