What weapons give most EXP with Siren upgrades?
I would suggest not using weapons as fodder, rather craft the Element gems for weapons (inventory / transformation button, top of the list on the left). They give far, far more xp and only cost 1cp to use. They can be a bit costly to make, but you won't need many; like 5 soul stones, and 20 powders + 50sp for 1 Element gem. You might need 4-6 to go from stage 1 to stage 10.
If you want to use actual weapons, then the blue weapons (cold iron) from Poh 24 might be the best / least costly.