Choose a main weapon
Early titanite is limited. Pick one weapon with a comfortable moveset and meet its requirements, then upgrade it regularly. Keep a backup for a different damage type, but avoid spreading every new shard across five experiments at once.
Understand the upgrade paths
Most ordinary weapons use Titanite Shards, Large Shards and Chunks before a Slab at +10. Many special weapons use Twinkling Titanite or Titanite Scales and finish at +5 with a Slab. A special +3 weapon and an ordinary +3 weapon are not at the same relative stage.
Protect your health investment
Once requirements are met, more Vigor can be a better early purchase than a small scaling increase. Upgrading a weapon improves its base damage without taking levels away from health and stamina. A caster should remember to upgrade their casting tool too.