Elemental Stones
Your (boring) mission now is to collect various equipment to help you farm for items.
Consider farming elemental stones to infuse your weapons. Some useful elemental stones include Boltstone, Faintstone, Firedrake Stone, and Darknight Stone. The Basilisks at Things Betwixt can be farmed for various elemental stones. Increase the drop rate by equipping these: Watchdragon Parma, Prisoner's Tatter, and Prisoner's Hood. Consume a Rusted Coin before each farming round to further boost your item discovery.
Infuse your weapon with a Raw Stone to give it high base damage output at the cost of decreased stats scaling. In some cases a raw weapon can result in lower damage output than the same un-infused weapon. For example, the Raw Mace+10 and the Mace+10 each deals a flat damage of 288. Equipping the Vessel Shield, Strength Ring, and Dexterity Ring raise the damage output of the Raw Mace+10 to 291. Further equipping Cale's Helm doesn't raise your damage output. The same setup would result in the Mace+10 having a damage output of 301, ten more points than the Raw Mace+10. Now suppose you equip the Vessel Shield, Flynn's Ring, and the Ring of Blades+1. The Raw Mace+10 would have a damage output of 373, whereas the Mace+10 would deal 376 in damage. A difference of 3 points, but the Mace+10 is still doing slightly more damage than the raw version. Both the Mace+10 and Raw Mace+10 are outclassed by the Raw Homunculus Mace+10. In general, infuse your weapon with a Raw Stone and use Flynn's Ring and the Ring of Blades+1 to boost your damage output. Equip items that raise your Adaptability and Endurance.
Heide's Tower of Flame
Your objectives at Heide's Tower of Flame are: (1) obtain an equipment for farming; and (2) open the path to No-man's Wharf. Satisfy the first objective by fighting the Guardian Dragon, which drops the Watchdragon Parma upon defeat. This shield is useful for farming rare items. Defeating the Guardian Dragon would unlock the fight against Old Dragonslayer. There is no reason to face this boss now because your damage output is paltry and you require the Rapier to easily defeat the boss. Instead, fight the Dragonrider to open the path to No-man's Wharf.
Dragonrider
SL1 Cheese the Dragonrider at Heide's Tower of Flame
SL1 Dragonrider at Heide's Tower of Flame
The Dragonrider can be cheesed by baiting him into performing a thrust attack while he is near an edge. His thrust attack propels him forward and the momentum carries him over the edge. Even without the cheese tactic, the fight is easy as long as you position your character behind him. Constantly strafe to your right, avoid any attack, move around to his back, and get in one hit. Rinse and repeat. The Mace is recommended for this fight.
You must defeat the Dragonrider to have Licia be your merchant. Licia opens the path to Huntsman's Copse, where you can farm a Prisoner's Tatter. Defeat the Dragonrider, exhaust Licia's dialogue, rest at the Tower of Flame bonfire, and Licia should relocate to the Rotunda at Majula.
En route to No-man's Wharf, locate a Sublime Bone Dust underneath the Tower of Flame bonfire. From the bonfire, proceed ahead to a hallway and make your way down a staircase. A Royal Guard is protecting an iron chest. Defeat the Royal Guard or lure him far away, then open the chest and grab the Sublime Bone Dust. Each Sublime Bone Dust restores more HP each time you use the Estus Flask. At base HP, you want each use of the Estus Flask to fully restore your HP bar. Collect as many Sublime Bone Dusts as you can. Ride the elevator down and light the Unseen Path to Heide bonfire.
No-man's Wharf
Treasures at No-man's Wharf, Dark Souls 2: SotFS
You need to collect some items in preparation for other areas in the game. One important item is the Fragrant Branch of Yore, which is required to unpetrify Rosabeth and open a path to various late-game areas. Dark Pine Resin x 3 are found on a corpse. As you are unable to purchase Dark Pine Resin for the rest of your playthrough, having Dark Pine Resin x 3 is better than none at all. Titanite Shard x 4 and Large Titanite Shard x 2 are available to be collected. You don't need to hunt around for Large Titanite Shards because McDuff sells an unlimited number of these. At the moment Lenigrast sells at most Titanite Shard x 10. Collect the Titanite Shard x 4 with a view to upgrading the Rapier to +3. The Greatsword is found inside one of two chests in the upper floor of a building filled with Darkstalkers. Despite being SL1, your character can still two-hand the Greatsword once you have collected the Vessel Shield and the Strength Ring. Use the Greatsword to easily dispatch of enemies that would otherwise be difficult to handle with the Mace or Rapier.
You will meet Gavlan for the first time. Have at least 10,000 souls to purchase all Poison Knives and Poison Arrows. These poison projectiles will be used against the Elite Giant x 2 at the Black Gulch. No-man's Wharf is where you should interact with Lucatiel for the first time. Interacting with Lucatiel here and following her quest line would reward you with the Ring of Steel Protection+1. You don't need to summon Lucatiel for the fight against the Flexile Sentry or any other boss. Exhausting her dialogue is sufficient for her to relocate to the Lost Bastille. There's no need to fight the Flexile Sentry now, but you can defeat this boss to open an alternate path to the Lost Bastille.
Huntsman's Copse
Visit Licia at the Rotunda at Majula, talk to her, and choose to move a path. Pay 2,000 souls for Licia to open the path to Huntsman's Copse. Have the path open, navigate to Huntsman's Copse, and light the Undead Refuge bonfire. Felkin the Outcast is found sitting near the bonfire. As your character's Intelligence and Faith are each 6, you won't be able to purchase Dark Pine Resin from Felkin. Leave him alone for the rest of your playthrough. Dark Pine Resin can be farmed from Undead Citizens at Dragon Aerie or consider infusing your weapon with a Darknight Stone.
Equip the Watchdragon Parma and farm the Undead Prisoners and Undead Laborers for the Prisoner's Tatters and the Prisoner's Hood. These two items together with the Watchdragon Parma should provide you with decent item discovery. Your farming route is the path between the Undead Refuge bonfire and the Bridge Approach bonfire.
Things Betwixt
Farming Faintstone, Firedrake Stone, and Darknight Stone
Start from the Fire Keepers' Dwelling bonfire. Navigate to the Basilisk nest where you previously collected an Estus Flask Shard. Equip the Watchdragon Parma, Prisoner's Tatters, and Prisoner's Hood. Farm the Basilisks for these upgrade materials: Boltstone, Faintstone, Firedrake Stone, and Darknight Stone. Purchase more Maces and Rapiers from Lenigrast and infuse each weapon with a different elemental stone. There are various reasons for infusing each copy of your Mace and Rapier with an elemental stone. The first reason is weapon durability. It might happen that you use your Mace or Rapier so much that its durability has become low. In this case, switch to an infused Mace or Rapier. At this early in your playthrough, you don't have access to Wellager to purchase Repair Powder. The second reason for having various weapons infused with different elemental stones relates to boss fights. You might find that a boss might not give you enough time to re-apply a weapon buff. Simply equip an elemental infused weapon prior to entering the boss arena and concentrate on the fight itself, without being distracted by the thought of looking for opportunities to re-apply a weapon buff.
Use McDuff's services to infuse and upgrade your weapons. Spend at least 14,000 souls on his services, exhaust his dialogue, and he would gift you a Titanite Slab. This is your second slab.