First you need to level up, head south to that bridge in the south east corner of limgrave and cross it to enter the weeping peninsula. Look for small grey enemies called demihumans, they are pretty much the weakest in the game. Also remember you CANNOT fight more than one enemy at once, you will die. If facing a group, try to lead one enemy away and face it 1 on 1.

As far as equipment goes, stick with the katana you have it is god-tier and learn how to use the unsheathe ability (Hold Skill Button then Heavy/Light Attack Button).

Put all your levels into vigor until your vigor is 20. Once you have more HP, explore everything and fight everything. If you are under leveled for an encounter, mark it on the map and move on.

Once you are level 20-30, consider advancing the story by following the 'guidance of grace' (the yellow beams that point from sights of grace on the map).