Okay, so non-spoiler hints: First, the Ring is in Heide's Tower of Flame, which will probably be the area you go to after the Forest. Cleric has a mace, doesn't it? If so you should have no problems in the Tower.
Second, to get more Estus you need to find Estus Shards. In the original version you can find 12 throughout the course of the game, but you can only use eleven of them. Give them to the Herald to get one extra quaff from the flask. You should be able to find one in Majula and I think there's one in the Forest somewhere as well. You can also increase the amount each quaff heals with Sublime Bone Dust. If memory serves, the first one of those you find will also be in Heide's Tower.
Third, get your agility to at least 90 and preferably about 100. Put points into ADP (and ATT, for a lesser effect) to increase agility. Even if you don't plan on dodge-rolling, agility also increases the speed at which you chug estus and use other items. It can potentially save your life.