Caressing prayer is funny and very hard build to do (imo). But nonetheless it's really nice and interesting way to beat the game.
Main thing is that you always count on strangers who helps you on your journey! Go to harvest valley after you defeat dragonrider, old dragonslayer, last giant, pursuer and join to sun covenant. After that you are free to help other undead warriors in their journey!
Offer your souls to the gods!
Just mace. Probably
Lightning Priest's Chime +10
Clear bluestone ring
Ring of prayer
Southern ritual band
Great Heal, Great Heal Excerpt, Great Lightning Spear, Lightning Spear, Heal, Med Heal, Sacred Oath, Soothing Sunlight, Sunlight Spear
Do the dragonrider early, get on 6000 souls lightning spear from Licia. Level up your faith to 22 by using his soul and you are good to go! This will allow you to go early Harvest Valley and join to Sun covenant.
Use white soapstone to level up your covenant rank and after you get your sunlight spear go to Blue Sentinels and rank up +3 in order to get Bountiful Sunlight (if you want this). Help other undead warriors by healing them, cast lightning spear and have fun!