Difference taiwanese mandarin vs. simplified mandarin?

This might be a really stupid question but well... For the context. I'll be doing an exchange semester in Taiwan later this year. I currently don't speak mandarin and for university in Taiwan I won't need it, since all my courses will be in english. However I've read that older people often don't speak english, so I'm thinking about doing a madarin course before I leave for Taiwan. It would just be a basics course, my goal would be to be able to order a coffee. I obviously don't expect to get even close to fluent in less than half a year. 😅 However all courses available in my area are taught by people from the PRC, so simplified mandarin. So my question how big are the differences really? Especially talking about the basics does it really matter if the course is taught by a person from PRC? (I would also do another course once I'm in Taiwan btw)