Reroll targets

Following list contains unit recommendations broadly agreed on by the community, intended to help players starting out.

Keep in mind that due to variety of game modes and damage types there can be no universally applicable tier list, so the suggestions listed are a matter of opinion and are meant to be a starting point rather than a definitive guide. This list covers Regular pool students (the ones that can be gotten from gacha at any time); limited and anniversary students can also be extremely strong, so if you are rerolling during any limited banner consider those as well.

The initial tutorial 10-pull is limited to launch unit lineup and guarantees at least one 3-star student. Japanese version of the game now allows you to retry your tutorial 10-pull up to 10 times, making getting any of the launch 3-star units relatively easy; of those units Shun is highly recommended.

Who to choose?

Recommended students that remain extremely valuable through endgame
Himari 3	Himari is a premier buffer that also brings in the valuable Cost Recovery boost. Notably, she does not replace Ako and is often paired with her. While not as impactful at the earliest stages of the game, Himari and Ako remain pillars of teambuilding later on.
Ako 3	Ako won't help you too much when you're starting out, however she becomes a must-have for anything outside of PvP eventually. Ako is a buff support character who increases characters' crit damage stat. Crit damage has, since launch, proven to be a king stat. She targets one character for a fairly low cost, and makes them exceptionally powerful. Also, she heals a party member every half minute or so, which really comes in handy. Not farmable.
Shiroko (Swimsuit) 3	Shiroko (Swimsuit) provides Cost discount for your team and is a competent single target damage dealer in her own right. Sees a lot of play in Arena and secondary Raid teams.
Shun 3	Shun provides skill cost boost at the beginning of combat. Core PVP unit; sees some play in Raids and Normal/Hard/Challenge missions for extra fast clears or as a general purpose Explosive damage dealer. Not farmable. Recommended pick from the tutorial 10-roll.
Ui 3	Ui can cost of a single strikers' ex skills by half (rounded up for odd numbered costs) for 2 uses of that skill, which valuable for high end game content.
Cherino 3	Cherino has a really useful EX skill (a humongous yellow screen clear) that gets discounted Cost when maxed out, and brings along the Cost Recovery boost that will allow you to cycle EX skills faster. She has yet to stop seeing use. Not farmable in practical terms, though launch players will have had a chance to "farm" enough of her fragments by 2nd year anniversary.
Generally good
Hare (Camping) 3	Hare (Camping) provides Himari-like Attack buff while being a Striker. She is still very new as of 3rd anniversary, but is expected to be impactful on the meta going forward.
Kayoko (New Year) 3	Kayoko (New Year) is a strong Mystic damage buffer. The nature of the buff makes her somewhat niche, but extremely valuable for the right content type.
Iroha 3	Iroha is a powerful Mystic damage specialist with a somewhat overblown and subsequently undersold reputation. Iroha is not farmable and is exceptionally strong. However, Iroha's most useful content is against the raid Perorodzilla and within Arena.
Iori 3	Iori has very high damage output at low EX cost. Performs well in PVP and in Raids against Heavy armor bosses. She is farmable from 2 late-game Hard nodes, but having her early on is a very significant headstart. As of 3rd year anniversary Iori remains a versatile Penetration damage dealers, though she faces significant competition from other character, most notably Mika.
Aru 3	Aru is an Explosive damage unit who eventually becomes so powerful that she's meta. At the start, she's a solid if somewhat unwieldy pick. She has an AoE/single target ex skill which can either hit a lot of people or just one. Farmable on later stages (from Hard 18-3), requires Unique Gear for endgame viability.
Haruna 3	Haruna is a Mystic damage counterpart to Iori. Just like Iori, her EX can devastate enemy teams in PVP; solid damage dealer in blue raids. She is easier to farm (hard stages 8-3 and 12-3) than Iori, which makes getting Haruna from gacha less of a priority.
Tsubaki 2	Tsubaki remains one of the sturdiest and most versatile tanks, despite being a launch 2-star. Extremely hard to deal with in PVP early on, remains a frequent PVP unit as of near 3rd anniversary. Isn't farmable until later (Hard 15-2), but given rarity you are likely to get her during initial pulls. Has a taunt that is extremely useful.

Who else can you use?

Following units are either farmable through various means, or relatively easy to obtain due to lower starting rarity.

Serina 1	Serina is your primary healer. Extremely versatile and easy to use, she provides excellent single-target healing, 2-cost EX skill can also be used to reposition units. Does not need high investment early on, but becomes increasingly important in later raid content. Core 1st season PVP unit.
Yuuka 2	Yuuka becomes an extremely competent tank with lategame equipment and her her Unique Gear, despite being somewhat lacking early on.
Kotama 1	Kotama provides valuable Attack buff for your Strikers. Sees a lot of play in raids.
Maki 3	Maki, obtainable from the raid shop. Provides Defense shred and solid single-target damage output for Binah raid.
Akane 2	Akane, obtainable from the raid shop, is another source of Defense shred. Does same Penetration damage as Maki, but trades damage output for a higher Defense reduction with better debuff uptime. Akane and Maki can see some play on other raids early on, but with Azusa and the limited Azusa (Swimsuit) providing similar Defense reduction effects in other damage types, their niche is primarily Binah raid.
Nonomi 2	Nonomi is a free unit provided through starter campaign. Widely used for story content, clearing EXP Commissions, and sees play in Chesed raid. In a pinch, she can be used in PVP early on if you are missing better damage dealers.
Serika 2	Serika the 120-yen cat can be bought outright with a starter package or easily farmed. A well-rounded damage dealer, high investment Serika sees play in quite a lot of Red content, though there are quite a lot of Red girls nowadays who can make her somewhat obsolete.

Note that characters sold in Raid and Arena stores are relatively easy to max out in a few months of play.