Not knowing your stats or play styles I’m not sure what to suggest for you beyond checking the merchant already listed. Different stones are good for different upgrade paths.
Sharp/hard stones for basic upgrades making all stats generally better while not altering or raising one more than another.
Blade stone makes weapons benefit more from Dex stat at the cost of str bonus.
Clear stone makes weapons gain more from both str and dex but lower increase in base damage
Grey stone makes weapons benefit from Str but drops off the Dex bonus
Moon stone adds magic damage to a weapon and also makes it gain power from magic stat while still allowing for a minor bonus from dex and str.
Darkmoon stone adds magic damage And MP regen effect, it too makes weapons gain from magic stat but removes dex and str bonuses. Weapon must be drawn to gain regen benefit.
Faint stone adds magic damage And HP regen to weapons, it also allows Faith to increase weapon damage, it lowers the bonus for str and dex but doesn’t eliminate them.
Mercury stone Makes weapons able to poison adds a little more dex rather than str
Sucker stone makes weapons able to cause Bleed adds a lot more dex rather than str.
Marrow stone adds a higher critical damage mod while lowering base damage.
Dragon stone Adds Fire damage to weapons but removes all bonuses from stats, you still need the base weapon stats to equip it wield it properly though.
Spider stone is for bows and it makes them gain alot more from Dex it also increases their range slightly at the cost of a slightly lower base damage and a lower strength mod.
Cloud stone is for shields and increases magic damage resistance at the cost of making it easier to break the block, it stays at default level rather than being able to withstand harder hits at higher levels.
Personally I liked faint stones on my first play through, found a mace that I upgraded to +5 with them. Couple the health regen with that of Abjudicator shield and the regen ring I found it a bit easier to tank things.
Oh yes an important note, Bladestone trying to farm for a Pure one to get +5 will drive you insane as it only drops at a very low rate from two monsters.
Quick edit - It is possible to get through without upgrading weapons to the max level or at all if you learn the patterns, it just makes it easier. Also, the Meltstone reverts any upgraded weapon back to it’s base form but you lose all the souls/stones that you invested in it to upgrade.
