You probably won't do it on your first playthrough, but that's ok. I'm doing a second playthrough of persona 4 myself but here's my general advice.

• Get dungeons done ASAP, do a good bit of training if you can so you can do all you need in one day and just chill.
• Do not skip through the dialogue, the story's pretty good and you want to make sure that you pick the polite option. Especially in persona 3 where the protagonist can sometimes be brutal.
• This includes class as well. There's no shame in looking up the answers and doing well on tests makes you more popular.
• If this is your first playthrough, I'd recommend finding what social links you want to prioritize. In persona 4 it's going to be obvious with the party members.