League of Legends: Items from the start.

So to begin with, you start a match of league with 475 gold (not considering runes/masteries/etc.) and get passive gold after minions spawn, 1:30 into game. Items from lowest price go like so. Starting at 35 gold you have your health and mana potions. The game only allows 5 of each to be carried at any one time, and they both have a pretty low set amount of mana or health restoration that falls off later in the game, but I would pick one or two up at match start. Then for 75 gold are sight wards. Sight wards give you a 3 minute vision over an area you would get if you were there. So they allow sight but not of invisible units or inside brushes. At 125 gold vision wards, which are the exact same as sight wards except they can see other invisible units, even other wards. At 180 gold you have your fairie charm and rejuvenation bead. The charm provides permanent +3 mana regen per 5 seconds, and the bead provides +5 hp regen per 5 seconds. Then you get to 250 gold and your blue pot. The blue bot gives you a short buff which provides extra AP dependent on your level, and a set cooldown reduction.

At 300 gold you have a hunter's machete which is a jungler item that gives bonus damage to monsters in the jungle. Also at 300 gold is cloth armor which is +15 armor. Then at 325 gold you have basic boots which give a small bonus to your movement speed. At 350 gold you have a red pot, basically the same as your blue pot, but instead more AD and HP dependent on level and no cd reduction or bonus AP. Then at 400 gold you have several items. Dagger, Long Sword, Brawler's Glove, and Doran's ring. Dagger is a bonus to Attack Speed, Long Sword is +10 AD, Brawler's Glove is +8% critical chance, and Doran's is +80hp/+20AP/and passive Mana regen over time and on minion kills. At 435 gold you have your Amplifying Tome which is +20 AP. At 440 gold you have your Doran's Shield which is +100hp/+hp regen/-8 damage by champion auto attacks. At 475 gold you have Doran's Blade, which gives +10AD/+80hp/and 5hp on auto attacks. 

Next week I will go into the items that start to require other items to be built, just a quick side note on that, items that have other items needed get cheaper the more items underneath you have, and you can have part of an item in your final item slot and still make it into what you want even if you have no more room.