The starter knight sword is viable till endgame, and you can buy shards later on, so feel free to upgrade it if you want to. People use Uchigatana because they may like the moveset more.
When infusing, take into account the base damage drops, but the scaling damage may go up (the + parameter next to the base damage).
So, if you're leveling DEX, and infuse the weapon with a Sharp stone, even though they base damage drops, the DEX scaling for the weapon goes up, compensating the loss of base damage and resulting in an overall greater damage at the end.
There's also stones that add, for example, fire damage, that will also drop base damage but add a secondary fire damage.
Can't remember any locked door that you can't acces there at the start...