I just got to the part where I really have some choice as to what to do with my time in game and I'm completely overwhelmed. The game keeps pointing towards this ominous day when the fog comes and I'm going to have to be ready to go save a person but I don't really know what i'm supposed to do in the meantime. Train? And if so where? Where do I buy items to use on this quest like potions/etc?
I'm also kind of lost on the Persona system and how I'm supposed to be using this Compendium and fusing these things. Am I just too early in the game to be worrying about this stuff? I haven't played an RPG in 10+ years and it's a lot of info to process at once.
I'm on Normal so am I basically going to be able to just wing it and have a good time or do I really need to start formulating a strategy? I'm really digging the characters and story so far but I don't want to run into some proverbial wall and not be able to finish it.
Sorry for all the questions.
Fog/Clearing Dungeons
It's best advised to get the dungeon segments out of the way as soon as they come up. So hop into the dungeon, grind until you're at the boss' level (people on GAF can help you work out a boss level, and failing that there are guides out there), then take the bastard on. I wouldn't leave dungeon crawling until the rain/fog, because that leaves you with extremely limited time if you screw a dungeon run up and have to evacuate until the next day. For example, you could encounter a tough enemy that decimates your party, and you have to run away and then evacuate the dungeon using Goho-M. There's probably not much you can do at that point, especially early on in the game before you get a certain Social Link that allows you to buy dungeon healing, so you'll have to exit the TV and come back the next day. If you're perilously close to the deadline, that could screw you over big time. So tackle it early to mitigate these issues.
As for the fog itself, it sets in after it's rained for several days in a row. When you look at the weather forecast (check the TV downstairs) and see it's going to rain for a few days in a row, you'd best get your arse into gear and clear the dungeon. However, if you do screw up and you miss the deadline, the game lets you rewind time by 7 days, which is more than enough time to fix everything up (as a reference: once you get used to the game's mechanics, you'll be clearing dungeons in one day on Normal difficulty).
Personally, I prefer clearing a dungeon on the first day or two that it becomes available, just so I can get on with the social links part of the game until the next dungeon opens.
Activities Outside of Dungeons
Talk to people in school/in Inaba. Get a job (jobs board is near the Chinese restaurant, item shop, weapon shop and so on). Strong Social Links help with fusing Persona of the same arcana. Don't forget to improve your skills too (like intelligence, diligence, and so on), as these are required to be at a certain level to unlock certain Social Links; you won't click with certain characters until you have a certain level of intelligence and understanding, or whatever.
Of course, whilst these Social Links have benefits in fusion, they're also amazingly well-written (on the most part) and worth doing for their own story line.
If you do a social activity with any of your Social Links, that takes up time and you won't be able to go into the TV on that day (unless it's an evening SL, like your job or Nanako/Dojima).
Fusion
Fusion is simple: you combine Personas to make stronger ones. Eventually, your Personas will run out of new abilities to learn. At this point (or even before) you can fuse two (or three, or even more later on in the game) together to make a stronger Persona. If you had a rare/favourite ability on an older Persona, you can carry this ability over to the new one, but many strong Persona will have stronger versions of abilities that weaker ones have, so be judicious about which ones you bring forward. The game will let you pick which abilities to carry over (this is on P4G only; on P4 for PS2 it's random). A fused Persona will get bonus EXP if you have a Social Link in the same arcana that you're fusing into. If that's a Lv1.Social Link, the EXP bonus will be small. A Max.Social Link will give lots of EXP. This is the best way to level up Persona, as they take a lot more experience to level up through battles than party members do.
You do all of your fusion in the Velvet Room.
Items
Items can be found in dungeons. You can also get some items in shops in Inaba. There's a weapons shop and a general goods store that stocks health potions and other aid items. Items for SP recovery can be acquired from one of the vending machines, but they're extremely limited in how much SP they restore, and how many you can buy. The best SP recovery items are acquired in chests.
The weapon shop is essential. You sell the weaponsmith materials you picked up from battles, and he crafts them into new weapons. You should probably visit regularly, sell him all your raw materials (they are useless for anything else), and pimp out your characters with new gear. Generally, the newer it is, the stronger it'll be/more protection it'll add, but there's a handy comparison feature when buying items that let's you see which stats go up and down with new each item you equip compared to your currently equipped one.
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It may seem like a lot to take but, but just take your time to learn all of these things. I guess you can get the hang of it in less than 4 hours, and that's a really conservative estimate. You'll probably pick it up quicker. By time you're on the second dungeon, all of this will be second nature to you. Have fun!