Okay, so I downloaded the game and played with it a bit. I'm going to go with a strict no pay policy(because i don't want to reward stupid decisions). A couple of observations so far:
You can change the voices to Japanese(yay!)
You only start off with access to Sophitia, Mitsurugi and Siegfried(boo!)
The announcer sounds like one of the guys from Honest Trailers(umm...?)
You start off with no clothing but underwear(I sense a lot of people starting with Sophitia for some reason)
There is a sort of kind of multiplayer component, in that you can use someone else's character in tag team.
You have a currency called AP that are used to start fights and regain health on a rematch.
This currency replenishes itself at a rate that should be satisfactory unless you start losing a lot(a match seems to cost 2 AP, and you replenish 1 AP every 2 minutes).
While you can't make fully custom characters, I've already seen one Sophitia on the tag team partner list with different hair and steampunk goggles, so I'm not sure to what extent customization goes yet.
The shop exists, and the tutorial shows you how to get to it(it's a menu item. not too hard to figure out). After that, no mention of it is made, so it isn't shoved in your face at least.
From what I can tell, you don't buy specific items. It's more like Mass Effect 3's multiplayer where you got a pack with random stuff in it. Moreover, these same packs drop from fights, so I don't see a real need for it unless you're just really impatient.
That's all I've got so far. By far, the most annoying thing is the limited characters. I'll play around a bit more when I have more time.