Best early weapons
There is no publisher-issued tier list. PC Gamer recommends Jagged Steel early because its bleed effect works well on many human bosses; the guide notes that some enemy types resist bleed until you find the Livingwood Talisman. Treat that as one useful build, not a universal winner.
The regional walkthrough lists Jagged Steel as a reward for defeating its namesake, Sanguine Twin near Yu'er, Dread Axe from Axemaster Peng Meng, and Hunter's Chain Sickle from The Hunt. Those give you different ranges and attack rhythms to try before spending more upgrade materials.
Sources: PC Gamer on Jagged Steel, PowerPyx collectible walkthrough, PBZ.gg weapon database.