I was just wondering exactly what gets transferred over to your new save file?

money , compendinum, your stats (like intelligence, courage, whatnot)
 
ability to battle secret  boss.
 
However you restart on level 1
 
might have left some out. ITs been a LONG time since i played P4

• Your Compendium and the Personae in it
• Your current amount of cash
• Your max social link items
• Your stats (courage, intelligence, etc.)

So I'd have to re-rank up with ALL of those people I ranked up with before?

if i were you, in your first playthrough i will put ultimate personas in the compendium and try to complete it cause whenever it was like 75% igor will give you a discount because you're near to completing you're personas... money time, and some events oh the best part IZANAGI----****NO----****OKAMI!!!! DUN DUM DUUUUUM!

Social stats.
Persona Compendium.
Persona Compendium discounts.
Persona slots (You will start with 12)
Max social link items (for fusing ultimate Personae)
Money.
Play time.

and i do believe the lvl limit only applies to fusing personae , so if your lvl 7 and want trumpeteer you can get him from your compendium. good thing money also goes over.

Also, with the high level personas that you acquired in your first run through, the first half of the game is piss easy so you might want to play on hard difficulty.

• Social Stats (e.g. courage, intelligence).
• Persona Compendium (every persona you've acquired with their levels and movesets intact).
• Persona Compendium discounts.
• Persona slots (you begin with the game's maximum of 12).
• Max social link items (gained from reaching social link level 10 with a social link friend).
• Money (yen).
• Play time.