Previous LoLU Lessons:
Lesson 1: Attitude
Lesson 2: Minions and the 1v0 Custom
Lesson 3: Champion Roles & Lanes
Lesson 4: The Things Novices Do
Lesson 5: Dealing with Smurfs

Note: Be sure to read the replies to this thread too, where several people argue with my choices, bring up good reasons for doing so, and generally elaborate on when to build what for the enlightenment of all.

My original plan was to cover entire generic builds for certain roles. That was shot down when a flame war erupted in the LoLU chat room over a good AD carry build. The AP carry discussion immediately went off on a tangent about Ryze, and by that point I gave up trying to get a good bruiser build. There is, however, something simple I can cover that will help you out immensely: items for that initial run before you recall for the 1st time. Novices make a couple stupid mistakes here that are easily rectified; once you do that, following the rest of the suggested item build is pretty effective.

What Not to Do with 475 Gold

Don't buy a Doran's first. I don't care what the Suggested Item Build shows, don't buy a Doran's first.

Why not?
Because then you can't buy health potions. The extra 80/120 HP is nothing compared to the extra 450-750 HP you get with pots.

So don't buy them at all.
I didn't say that.

Well, when do you buy them then?
Second. You buy them second. You buy them second, and third, and perhaps even fourth. Once you've got some spare cash to buy a Doran's and a few wards/pots with one Recall, that's when you start buying them.

Wait, 2-3 Doran's?!
Yes. Doran's items provide a nice early/mid-game boost for laning, plus they're a cheap way of filling up those extra item slots until you buy bigger items. While your rival holds off on buying anything to get a BFS, you can lay waste to his minions and pelt him for 90-100 damage a shot.

A good rule of thumb for laning carries is "buy at least 1 Doran's, buy more if you're losing the lane."

What to Do with 475 Gold

There's 3 initial item sets that cover nearly every role, including jungling. I'll list them below, then explain why they're used so often.

Boots of Speed (Movement, 350g) + 3 Health Potions (Consumables, 105g total):
The standard build for 2 reasons:
1. Everyone buys boots eventually.
2. Speed kills. Speed saves. Outrunning your rival is key. Being outran by your rival is a death sentence.
Great for any ranged champion and several melee champs.

Cloth Armor (Defense > Armor, 300g) + 5 Health Potions (Consumables, 175g total):
Lets you soak up 750 HP worth of harassment without recalling (and cut down the damage coming in in the first place). Mainly for junglers that want enough survivability to get through those first few levels, it's also useful for certain melee bruisers that expect to take a lot of punishment in-lane.

Faerie Charm (Magic > Mana Regen, 180g) + 3 Sight Wards (Consumables, 225g total) + 2 Health Potions (Consumables, 70g):
The standard item build for bottom-lane supports. Why the strange combo?
1. Faerie Charm is one part of the Philosopher's Stone, the first item built on most supports. Its mana regen also lets you shoot off more spells to support your laning partner.
2. Sight Wards shut down hidden attacks from the bushes. Sick of that Nidalee throwing spears from the bush? Toss a ward down. Makes the lane much less stressful.
3. Health Potions should be self-explanatory by now.

Some variations on this involve buying less wards & more potions, or swapping the health potions for mana potions, or just going easy on the wards & potions to buy that Philosopher's Stone faster. Good for supports that worry more about supporting their partner than darting in & out fast.

If you know those 3 initial item sets, you can use one of them on just about any role you need to fill. Alright, so the initial items are covered, but what about skills? We'll cover your initial skills in the next lesson.

You should add in a section about going back with a bit more. I often find myself skipping dorans altogether because I'm going back with 1k plus and can get something a bit more immediately needed as well as wards and pots.

It depends how well you're winning lane when you recall with that much gold. The debate over Doran's vs items you can build with boils down to "how much help do I need now?"

Need a lot of help now = Doran's
Don't need much help = other items

Doran's is a strong starting item for an AD with a sustain support, especially against a non-sustain support (which is more likely to be a kill lane, i.e. you want the burst protection).

The thing is, with the extra health from a Doran's, your healer doesn't need to worry about topping you off; they can let your regen (and lifesteal) do some of the heavy lifting. When you're less 100 health, every point of health matters.

Depends on your lane opponent. Remember dorans give a really huge amount of stats for not very much gold. I don't know if bruisers go double dorans anything, though - I'm no good with bruisers in general.

And yes, I've bought double dorans wards pots on a trip back with 1k+ before. Let's see what else other champs get.
Poppy gets Sheen.
Yorick gets Tear.
Supports probably get either the boots upgrade or kindlegem...or forego both for more wards. Assume both gp10s are already in play.
A few mages get Catalyst.
Every other time, you get the boots upgrade and another doran item, or just double dorans.

I'm not saying the health you get back is huge, but it's definitely something to note; I also tend to harass the enemy with auto attacks, so I get a bit back from that as well.