Do the tutorial once, then go to the settings and delete your account. The game will kick you back to the main menu and let you proceed to make another account. From now on every time you make a new account on your current device the game will ask if you want to skip the tutorial. If you click no you'll have to do the tutorial again, so watch out.

In order of importance:
1. Pluvia Madoka (not to be confused with Lux Madoka, which is a free unit)
2. The girl you like best
3. Concentrated Missile Strike Homura
4. Kaede or Sana
5. Mami, Mabayu, or Time Stop Strike Homura

In more general terms, Pluvia > Powergap > Homu > Healer/Tank > Speed buffer. I would highly recommend prioritizing Pluvia over everything else. Buffers are only worth keeping if you also get a 5* attacker. The game starts you off with one random 5* and rerolls are pretty fast, so I would recommend trying for at least three in total.

Most characters are not limited, but if the current banner character is then you may want to aim for her as well. Starting with two breakers is pretty good, two attackers is okay, two tanks is useless. Kirika and Sayaka are both fine substitutes for Sana. Yuma (4*) is an okay substitute for Kaede and is often better than Doppel Iroha. Ren is very good for some niche content but debuffers in general are not a high priority. Tsuruno is okay if you also get Mami or a crit-based 5* attacker like Yachiyo, otherwise skip her. If you want to optimize your 4*s, then try for Yuma (Healer), Hazuki (Buffer), Asuka (Attacker), Mito (Breaker), Kokoro (Tank), and/or Himika (Debuffer) to fill the roles you're missing 5*s for.

PVP is mostly for bragging rights, but if you're interested Felicia is essential. Kirika and Oriko are also good.

They're just numerical improvements, which can be impactful but don't change how characters work in any significant way. if you get some that's nice, but I would generally not recommend trying for them specifically unless there's one character you really like.