I asked this question around two months ago. I have since completed this game twice and I can confirm that there's an unlimited availability for all upgrade stones, each playthrough.
The hardest ones to get are definitely the slabs.
Regular Titanite Slab is a 100% chance drop off the Stray Demon, which you can battle on your second visit to Undead Asylum. Another slab is awarded for completing the Siegmeyer of Catarina sidequest. Although Titanite Slab is a rare drop off Crystal Lizards in the Great Hollow, it can also drop from Darkwraiths in New Londo Ruins, which respawn, making the supply unlimited.
Red Titanite Slab can be found in the Chaos Eater pit in Lost Izalith as a treasure to loot. It is also a rare drop off the Chaos Eaters themselves.
Blue Titanite Slab is found in the Crystal Caves as a lootable item. It is also a rare drop off the Crystal Butterflies in the same area, which respawn.
White Titanite Slab is found in the cave filled with Pinwheel Servants on a lootable corpse. It is also a rare drop off the Pinwheel Servants themselves.
I'll start off by pointing out that the Graveyard you find near the start of the game
is intended for a higher level player, so you should avoid it for now.
Both the Cleric and the Warrior are excellent beginner classes. The Cleric has healing, which is very helpful, but has very weak armor. The Warrior lacks healing, but has more well rounded stats for combat, and starts with better equipment.
When it comes to developing your character, there is one thing you should keep in mind: You should only boost one offensive stat. This includes: Strength, Dexterity, Intelligence and Faith. The reason for this is that most weapons have stat scaling. So if you have a weapon which scales with strength, and you decided to split your points between dexterity and strength, all of the points invested in dexterity are essentially useless. That isn't to say you shouldn't put any points into the other offensive stats, just that you should only be putting enough to meet stat requirements for equipment.
My personal suggestion would be to focus on a Dexterity build. This will allow you to use bows effectively, which can make your game a lot easier. Bows allow you to both kill and weaken enemies from afar, lure single enemies away from a group, and take care of archers as soon as you encounter them.
Best Answer
The cinematics are fairly plain, and don't reveal much of the storyline. You get carried off by a crow... you ring a bell... you ring another bell. It's all very exciting. (Sarcasm)
The real story can be found in the items you find, and by talking to the NPCs you come across. Talking to them after each major event (killing a boss, ringing a bell etc.) reveals more about the story, and the lore of the game than the cut scenes ever will. This is (in my opinion) what makes the game so enjoyable - not only are you fighting for your survival, but you are also searching for the clues that reveal what you need to do next.
Failing that, if you can't be bothered investigating it all, some youtubers like VaatiVidya have done a lot of good research into the story and it's characters.