Forms are the main power spike, and they are not free damage on every target. Use the race page for the list, then open your own form menu for the price. Only a few unlocks are printed with a level.
By race
Saiyan forms on the race page are False Super Saiyan, Super Saiyan, Super Saiyan Grade 2, Super Saiyan 2, Super Saiyan 3, and Legendary Super Saiyan. False Super Saiyan drops from Lord Slug. Legendary Super Saiyan drops from Friaza. Rage sets health to zero, drains the experience bar, and grants 30 seconds of invincibility. Awakened Fury raises basic melee scaling, attack speed, and clash power. A filmed account near level 145 got a large all-stat bonus from Super Saiyan and a larger one from Super Saiyan 2, and mastery stars were what pushed Super Saiyan 2 from 100 to 115 in that clip. Do not treat those two numbers as the bonus at every level.
Human forms are Kaio-ken x2, x3, and x4, then Max Power and Mystic. The first three Kaio-ken forms last no longer than 6 seconds and front-load damage, which is why the race page tells new players to avoid Human. Max Power drops from Banaras. A race video places Mystic at level 153 for the alien form set. The Human page lists Mystic and does not repeat that level.
Namekian forms are Potential Unleashed at level 70, Ultimate Namekian at level 145, and the giant form from Lord Slug. The form heading says Giant Namekian and the drop line says Great Namekian. Frieza forms are Second, Third, and Final. They can remain active instead of timing out, Ki abilities are boosted, and healing plus regen unlock only if you transform in order.
Majin has Purification. Jiren has Emotion, Half Emotion, and Full Emotion. Android has no forms. Tuffle has no form list. The alien subclasses Beerus, Saibaman, Yerdratian, Appule, Pikon, Generic, and the readable Mushroom list share Kaio-ken x2, Potential Unleashed, Max Power, and Mystic. Yerdratian also lists Gigantify, which Banaras drops for Yardrat forms. Yerdratian and Yardratian are the two spellings used for that subclass.
Mastery and the reward penalty
Day-one footage says mastered forms drain less Ki and give slightly better stats. That matches the Super Saiyan 2 star example above. There is no public table of how many kills or quests a star requires.
Killing NPCs while transformed pays less experience and Zeni. The game tracks damage dealt in the form, so dropping the form at the end of the health bar does not restore the full reward. Use base form on snakes, frogs, Saibamen, and other quest fodder. Transform for world bosses, raid targets, and players.
Rage is shared by Saiyan, Majin, and Jiren. It is a last resort: health hits zero and the experience bar is drained for 30 seconds of invincibility. Do not treat it as an opener.
Prices that are safe to repeat
Gum Gum Pistol is level 12 and 1,000 Zeni. Gum Gum Bazooka is level 60 and 9,000 Zeni. They are shared by Majin, Namekian, Mushroom, and Tuffle. Tuffle Possession is level 60 and 10,000 Zeni. Other form prices that appear on general tier articles were not repeated on these race pages, so they are not copied here. Buy from the form menu you can see.