Personally, I would not choose IOP. The entry can be difficult, even with low surf. I also feel it's not a great site for beginners. I think the deep stuff is a lot nicer than the shallow stuff there.
My personal preference is Osezaki. Clean entry, lots to see above and below water, and good for beginners up to advanced. Protected bay and nice gradual slope. Also has night diving on Saturday evenings year round.
Osezaki is a preferred weekend trip. Atami is an easy day trip.
My opinion, 2mm maybe enough for August through October, though depending on your body type and preferred depth, you could get cool. Personally, I think a 3mm is better, and 5mm is the best all round suit for Japan, I feel.
I've had good luck here with Jellies, though I am often in the US during much of August.
A full set of gear will run you 5 to 8,000 Yen at an operator. Some operators, like myself also have gear to rent, most likely a much higher quality than the dive site operators.