Finally got all the DLC downloaded. It's much easier to get stuff via the shop link from the main menu, but not everything was up when I started, so I went through the PS Store, which was much slower, since it would always go back to the top of the list when I downloaded something. I switched back to the in-game shop after doing this for 40 minutes and everything was there...except for Jann Lee's stuff, which I got from the Store, and the Hokoka costume pack. For whatever reason, almost all the costume packs showed as for sale and only the individual costumes came up as "purchased," so I couldn't take the fastest route. One of the swimsuit packs also shows as for sale even though I purchased it on PS3/Vita. Hopefully this will be sorted out in the next day or so.
Tried online briefly. Joined a 4+ connection lobby and it was GREAT! Noticeably better than PS3/Vita/360 were. Tried a 3+ connection lobby and it was pretty laggy, although it still felt better in comparison to PS3. Inputs still felt more responsive. I beat the host of this room with a perfect and he quit, which improved the connection a lot, LOL.
I need to play a lot more online to get a real idea of things, but if online has been improved overall, I'll be very happy with this purchase. Right now there aren't many people online. Hope that also changes. PS3 was always pretty busy, thanks to Core Fighters.
I also was able to redeem my Amazon pre-order DLC. Did this on the SEN website and see no indication that anything is downloading. Can't see anything in my transaction list on the PS4. Sigh...