Small priconne guide

Optimal rerolling picks
Makoto, Christina or Jun. These three characters are pretty core for everything you want to do in the game and most things are balanced around these characters. Some optimal guild war strategies rely on you borrowing a Makoto for the first round and Christina for the second round so you can use them on both rounds for an idea of how useful they are.
As for what they do

Jun: Strong tank with a shield that absorbs damage on her union burst. Her main selling point and why she's usually the go-to tank is because Jun has a small def down and a heal which makes her really nice for when you need a tank. Currently, Jun has a hard node that can be ran three times a day for pieces of her, would take around three months to farm her from scratch but its optimal/reccomended to just roll her and use those fragments to 4* or 5* her. Already had an event with farmable Jun shards.

Makoto: Queen of def downs since release. She comes with two defense down skills which are a must if you want your damage characters to actually deal damage which makes Makoto perfect and optimal for physical damage comps. Makoto is currently obtainable from the clan battle shop (and possibly the only character worth getting with said coins at the time of writing this) and hasn't had an event with farmable Makoto shards at the time of writing this.

Christina: The first princess fest limited crown. Her union burst is a damage skill that cannot miss and will always deal critical damage no matter what. Her other two skills increase her attack/TP gain while the other one deals damage and gives defense down which makes her peak performance when it comes to damage units. The only time Christina's skill can miss is if the enemy is in some sort of invincible/ghost form like Miyako's pudding form for example where its not that the skill misses but its more that the enemy can't take damage in that form. As mentioned, Christina is a princess fest limited which gives her a semi-limited status, she comes back every princess fest with doubled rates but you can only roll for her during fests and does not have any other way to be obtained outside fests.

Making your first team

You have five character slots to build your team. You will absolutely need at least one tank for your team and then four damage units. A healer is optional if you're having issues surviving but the idea is that you want to kill them instead of trying to stall to victory because you're on a timer for every battle and timing out means failure.
Its worth mentioning that starting rarity doesn't determine everything in this game so don't be put off or get locked into a mentality where you automatically think 3*'s are better than all 2*'s.

Common newbie 2* tanks are Miyako (usually referred to as Pudding) or Kuuka. 3* tanks are Nozomi, Jun and Ruka. You absolutely need one of these characters for you to not die because they will take most of the damage and allow your damage characters to survive.
Nozomi has an AOE heal skill and a taunt UB which makes her an amazing tank for story clearing, Kuuka has taunt skills which means she will be drawing most of the fire towards her which can cause her to die quickly sometimes so you may need a healer to keep her alive, very good when you need to tank magical damage. Pudding is a physical tank who is weak to magic but excellent when tanking physical damage because she can heal herself and turn invincible for a few seconds. Pecorine might do the trick for a tank if you got no one else but she only gets really good when you're able to get her personal equip which is a bit of a late game thing.
Shizuru is NOT a tank. She stands behind all your front lines and provides heals so she's more of a frontline support but absolutely not a tank.

Good healer options are Misato, Maho or Yui to keep your team alive. Misato gives regen to the frontmost unit and her burst is a team heal, Yui is a big burst heal on union burst while Maho has a single target heal on a skill.

Then you fill the remaining spots with DPS characters. There are a lot of DPS characters so there's a lot to pick from but common/top choices are Shiori, Kaori, Suzuna, or just fill with what you have. If you still want or need help about physical damage dealers then just ask or refer to a wiki like https://gamewith.jp/pricone-re/article/show/92923

Magical damage dealers are a trickier bunch, you only have a select few and there's not a lot of flexibility in what you can use. The core of most magical damage teams you will see use Summer Kyaru for her rare magic defense down and single target burst which was a 2017 limited but as a new player, your magical damage dealers will be more along the lines of Nanaka, Kyaru and Kyouka. If you can borrow a Summer Kyaru for things like guild wars then you absolutely should for an optimal magic team but if you cant then that's what you should work with. Nanaka is most likely going to be the savior of magic once she enters shops and can easily be 5*'d by everyone, Kyouka is a strong single target nuke and one of the cores of an optimal magic team, Kyaru is a decent mage who gets pretty nice with her personal equipment and Akari is a midline support that provides the rare magical defense down plus lifesteal on her union burst skill.

Actually doing things
You want to rush and unlock Very hard dungeon to have a nice dungeon coin income. You'll be placed in a new arena group and be notified of it after clearing one of the early worlds (Somewhere between 3 or 4) and princess arena unlocks after beating world 8. If you can't clear stuff then your main issues are in your team comp (Remember to have 1 tank with damage dealers. If you can't survive then you can replace one of the damage dealers with another tank or a healer like Nozomi, Shizuru, Misato or Yui for example) or just a case of being outgeared and needing to upgrade your character gears to the highest possible rank you can take them. There's a star button below the three big stars when you click a stage, clicking this button will show you team comps other players used to beat that map and can be useful for ideas. Keep checking it as the comps will constantly change as people run that stage with new/different things.

For characters that should be prioritized from the dungeon shop, you should definitely and absolutely buy out everyone from the dungeon shop and 5* them except probably Rin (the squirrel) that can be at the bottom of your priorities. Its up to you to look at what your team needs and decide who you want to buy first. If you're hurting for tanks or someone with a taunt then Nozomi should be your number one priority to 5*, if you need a healer then grab Misato or Maho and so on.

In other tips, do NOT waste your memory pieces. The best use for those dupe fragments you get when rolling a dupe are to use them on limited units, units that can't be farmed or freshly released units that you really want to use and won't be farmable for the next six months. If a unit is farmable then its optimal to farm them normally to 4* and 5* instead of wasting pieces on them.
Normally, you'll only take them to 4* with pieces because 5*ing someone is a very big investment and you should be 100% absolutely sure on what you're doing if you want to take an unit from 3* to 5*. Never ever attempt taking a character from 1-2* to 5* with pieces because its extremely expensive and every 2* will be in a shop eventually, this sort of thing is reserved for the people with too much money where stuff like this wouldn't set them back in the slightest.

Also, do your dailies every day and your daily resets. If you keep up with your arenas, its worth it to do 3 resets a day because the crystals from your arenas offset the cost of your daily resets but this is completely optional for faster progress. Where you should be absolutely pushing out those resets is during 2x/3x drop campaigns. Your first six resets are completely and absolutely 100% worth it during a 2x drop campaign and you are only missing out by not doing so, 100 resets are iffy but might be worth it depending on how desperate you are and everything past 100 crystal resets is whale land where really only the big spenders can afford to do those without breaking their bank.