Honestly I much preferred Persona 4, but that's just a matter of personal taste. Pick a difficulty you're comfortable with, since I know you have a hard time with dying in games and it can get pretty challenging for newbs like us who don't know all the tricks and stuff. Work on the social links you care about.

Also yeah, I'd do the dungeon in as big of chunks as you can. Hopefully you'll enjoy it and it won't feel super tedious to you. But I get very anxious about that stuff and they tend to take days away from you with no warning sometimes, so sometimes it may seem you have more time left than you actually do. IIRC they generally give you the night before time is up, so you could wait until the end or get it over with at the beginning