I only visited the shop as I unfortunately didn't have time to stop by the museum on this occasion. However, I would definitely recommend popping in, even if it's just for stamps (they sell them at the same price as the post office but have a selection of commemorate stamps - these are special stamps with pictures on instead of the classic queen's head design). The museum is a charity and is run by volunteers so as well as donations, bookings, it relies on shop sales to run.
In my short visit, I found the volunteers to be really friendly and helpful. The shop is small but there's a lot packed in! As well as the commemorative stamps mentioned above, of which they sell first, second, £1.70 bundles and E stamps, they also have mini sheets, FDC's (first day covers) and other stamp collectibles. They also had postcards related to the museum, PHQ cards (individual and full sets) and maxicards. They had such a good variety (better in fact than the Postal Museum in London) that I thoroughly enjoyed just browsing.
I am hoping to come back and have a look around the museum on my next visit to the city. But if you're in the area, pop in even just for a look around the shop - it's a real hidden gem if you're interested in anything postal-related!