which one of these is the most challenging to start with
I will have to say Cantonese is harder because it has more Tones, 4 in Mandarin vs 6 in Cantonese, than Mandarin, however Pronunciation is slightly simpler for english Speakers
Theres a lot more resources to learn Mandarin although depending on where you live there might be more Cantonese people to practice with. Generally I would suggest learning Mandarin first only because it is pervasive throughout the mainland while Cantonese exists only in HK, Macau, Guangdong, and basically every Chinatown where Mandarin also coexists. But you probably already know that. So go with whatever language strikes you the most or just flip a coin.
IMO neither is harder than the other. With regards to tones, Cantonese might have more tones but because Mandarin has fewer tones, to my (Chinese) ears the tones in Mandarin jump around in pitch a lot more and it is harder to predict what sounds right when you can’t remember the right tone (if that makes sense). Basically it is easier to be way off in your tones in Mandarin than Cantonese. With Mandarin you also have the distinctions between zh, z, ch, c, and other retroflex sounds that make Cantonese pronunciation easier. In Cantonese, you may need to learn how to pronounce the initial ng sound if you haven’t already (it’s fun tho).
This question might be off topic, but are Cantonese and Mandarin the same in writing? Are different phrases used to the extent that native speakers of these two Chinese languages could not understand each other?
I’ve read that Cantonese only uses traditional Characters while in Mandarin you have an Option to use either traditional or simplified Characters, mainland China uses simplified Characters and Shanghai and Taiwan uses Traditional Characters. Cantonese is said to be a very colloquial Language, so it means that the Language is always adding different types of slang which you can’t learn via a traditional language Textbook and thus you have to be in the Country to learn it.
I’m also no expert, but I hear the languages are quite different, and would be written differently, but Cantonese speakers often write in mandarin.