How to choose a weapon
A weapon gives you two things: base ATK that scales with level, and a secondary stat that usually matters more. A weapon whose secondary is CRIT DMG saves you an entire artifact piece; one whose secondary is Energy Recharge can fix a team whose rotation never closes.
So there is no absolute "best weapon": the best is whichever covers your character’s gap in the team they are actually in. Filter by weapon type and rarity, and read the passive before you look at the numbers.
Four-stars are not filler
Many four-star weapons — especially craftable ones and event giveaways — sit very close to five-stars at high refinement, and occasionally beat them on a specific character because the passive matches how that character plays.
That is why every character page carries an explicit "free / budget" line. It is not a consolation prize; it is the correct answer for a player who does not spend.
Refinement
A weapon’s passive strengthens with duplicates of itself. The gap between R1 and R5 is large on some weapons and marginal on others, and that is worth weighing before you spend ascension materials: an R5 four-star can outrun an R1 five-star.