I'm at the start of the game now, a bit past that (just about to enter Blighttown, ulp...) and have absorbed a fair bit of info. Some of this may not be ideal (way too many people just say "It's supposed to be hard, figure it out yourself" when I ask for help but this is what I learned.
There are definitely places you don't need to go in Dark Souls, alternate routes so sometimes as you get to an area you aren't supposed to get past it. In this case I'm afraid you are. The Dragon isn't that difficult but it is remarkably opaque, after it breathes you can dash (hold b as you run) into the alcove on the left side. At the very end (closest the dragon) its breath won't hit you, from then you can cross to the other side, go downstairs and unlock a shortcut back to the latest bonfire. Checkpoint!
If you start over pick a Pyromancer, and pick up the Master Key. The Pyromancer just plain has better or equal stats (for his level, which is critical for how the cost scaling works in Dark Souls) than anyone else, better equipment (that Pyromancers glove makes early fights a ton easier) and better armour (You have to play a long time before you get better light armour than the Pyromancers starter robes). That said if you don't want to start over don't sweat it, the other classes are only 2-4 stat points behind the Pyromancer.
Dark Souls is going to do horrible things to you pretty much all the time. If you get het up when you die even if you reclaim your body I don't think you'll get the most out of it. If you're getting souls you're progressing, even when you don't you're still making some progress just because you are learning.
Building your character. I can find almost no info on this, experts will just not give advice on how to build a PVE character. There are builds out there but they aren't peer reviewed. As a rule of thumb though I was told you want 40 end, 30 vit, enough Int, Dex, Str and Fth to use your weapon/spells of choice and leave Res at base.
Regarding choosing spells Pyromancy doesn't scale off anything other than improvements to your Pyromancy Flame so is useful if you are planning to use heavy weapons or put lots of early points into end and Vit. It says it scales off int, this is a lie, only the damage of the melee punch attack scales from Int and you don't want to be using that. Sorceries scale off Int and are a great way of doing lots of damage when you get to the basic spell trainer (You're sort of nearly there but he's quite well hidden, especially if you haven't found the Undead Merchant Male and bought the Residence Key), that's the one I'm using and I can see why people say it's easy mode, though it's still easy mode in Dark Souls so I'm dying pretty damned often. Miracles scale off Faith and contain healing magic. That's obviously very tempting, at least to splash into though I couldn't say if its a good idea as I haven't tried it. So far my flasks have been enough as long as I keep kindling the fires.
Regarding Kindling fires it's pretty much a good idea to do that all the time. Sooner or later you're going to lose that Humanity. As a brief guide it costs 1 humanity to become human, at which point you're going to be ganked in the next 20 seconds and go back to being Hollow, and a second Humanity to kindle the bonfire. You get humanity randomly by killing enemies anywhere you haven't killed the boss, so what I do is wait till I have 1 humanity, go back to the bonfire, use a humanity item to go up to 2 and use both to go Human and Kindle the fire. 10 flasks is a huge help in being sure I'm on top form.
Broken items! You'll be glad to hear you're near one, though it will eventually get outpaced by other weapons so it won't make the whole game easy, just the next bit. That may or may not be a good thing. Anyway when you get past the dragon (downstairs, you don't go actually past it remember) there's the shortcut to the last bonfire and up above that is a point you can snipe the dragons tail to get a sword called Drakes Sword which does huge damage for the part of the game you're in, but is very limited in how well it can be upgraded. There are guides on how to get it, (google Drakes Sword and you're sure to find them) but you'll need a bow and a ton of arrows (ideally heavy) the guide said it took 20 but I found it a really tough shot and ended up using over 40. This isn't cheap at this stage in the game but will be a huge help.
Also there's a really useful spear in the graveyard at the start. If you spend all your souls you can pick it up by running like a madman around the graveyard picking up all the shinies. So far I've always survived this, but the enemies hit hard and are basically immune to your attacks at that stage in the game. Spears are really, really great items in Dark souls as they don't bounce off walls and let you hit from a long way away, while blocking.
Lastly (not lastly there are more but this is getting a bit much already) at the next bonfire there's a chapel area. Inside, upstairs there's a knight in gold armour in a cell. Free him and a while later there's a quest to get some great items. Or you can kill him right now to get the Ring of Favour and Protection, pretty much the best ring in the game. It does disintegrate when you take it off though so be careful. He also drops an item you can trade with a merchant under firelink shrine (behind some bars) for improving your healing flasks.
