I feel way in over my head - I don't have a clue what confident arcane fusing stuff it keeps telling me about is. I'm absolutely lost as to the appropriate way to execute my personas, pretty sure I screwed something up big time in the first tutorial. I just got a part-time job... seems I was supposed to? But then the next day Ann is like "yo we better hurry the f up for the palace" so I just went back. Lots of systems, lots of "hope I'm doing this kinda sorta right."
Each confidant is associated with a particular arcane, much like every persona has an arcane it belongs to. For example, Ann's confidant is The Lovers, just like Pixie belongs to that arcane. This means that, should you produce a Pixie through fusion (or any other persona from that arcana), it will gain bonus experience after fusion depending on how high your confidant level with Ann is.
This means that it is beneficial for you to fuse personas which will get a lot of bonus experience, because that way they will learn new skills a lot faster than through random battles, and I mean
a lot.
But I do think the game kind of overstates the importance of this. Yes, it's a very nice bonus, but no, it should not deter you from fusing personas that won't receive bonus experience. Especially early in the game, when you don't have many confidants yet and their levels are low, you won't gain that much bonus experience anyway.
There isn't really an appropriate way to fuse ('execute') your personas, aside from trying to cover as many weaknesses as possible, especially for damage types your party members can't hit. With Ryuji, Morgana and Ann you have Zio (Electric), Garu (Wind) and Agi (Fire) covered, so you will want to look for personas that have access to Bufu (Ice), Kouha (Bless) and Eiha (Curse) skills. (There are two other damage types, but they won't really come into play until the 2nd palace.)
Don't worry too much about part-time jobs. They're a handy way to make money and raise certain social stats, and you will want to spend at least once every while working there because Persona 5 likes to hide at least 1 new Confidant and a couple of bonus missions behind them. But in theory you could apply for a job, get hired, never show up and nobody would care.
