I have fitted a new door to my shed and as you can see there is a big gap and it looks a bit ugly. How would you recommend I make this look better? Some sort of external trim? Internal door stop?
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Part of the "ugly" aspect of your door is that the gap is not uniform. The bottom hinge gap appears much smaller than the top. Correcting that by adding shims to the bottom or re-positioning either or both hinges to accomplish even spacing on that edge.
One can hope that in so doing, the gaps elsewhere will even out. That alone should improve the appearance, perhaps not requiring gap seals.
If the internal door stop refers to a need to prevent the door from turning inward too far, a wooden strip across the door frame, inside the building, hanging down only far enough to contact the closing door will provide an internal door stop of sorts.
There is an aspect to this door in that it is sagging down on the side away from the hinges. See comparative top and bottom parts of the picture.
This gives the impression that the door was probably built as follows:
If this is the case then you will want to add a diagonal brace to the door as shown below with its bottom toward the hinge side. This will prevent sagging like is showing in your picture. (Push the door back square before adding the brace).