Always make use of your time efficiently. Given the option, you should always be trying to raise your confidants or social stats. I'd look up all the various ways to up your stats, because some give back more than other. Doing activities that either give you very little benefits or non at all (like working out in your room to raise your HP) are not worth it in my opinion. Also, in regards to confidants, if you have a Persona made under the same arcana as the person you're hanging out with, your "best" responses will raise their level by one more note. For example, when you hang out with Tae, who is the death arcana, have a death Persona equipped.
Try and secure the route to the treasure within a day when possible. A couple of the palaces will kick you out for story reasons, but the more days you spend in a castle, the less time you have to do stuff outside. Same with Mementos requests. Tackle those a couple at a time. Getting SP Adhesives from Tae will help you greatly. Ranking her up to 7 will cut her prices in half, making the 3rd SP adhesive 50,000.
Sell all the junk you get in palaces to the Airsoft Shop vendor. Seriously. I played through a good chunk of 4 without knowing about that. Always strapped for cash, it was miserable. Speaking of that vendor, I found that upgrading your melee weapons and armor was way more valuable than guns. Like half way through the game I upgraded everyone's gun, then again at the end.
Don't get too attached to your stock of Personas. You'll run out of space to carry them, and the ones early on mostly suck. Always be fusing. If you find one you really like, you can power it up, but fuse, fuse, fuse. Again, in P4, I didn't know much about that and spent most of the game with the MC's main Persona simply cus I thought he looked cool. Not the best course of action.
