At the start of the game you start with 625 gold, and 825 if you random. What you spend this money on is entirely dependent on the hero you are playing, the role you are playing him, the lane you are playing them in, and against the heroes you expect to be against.
Predicting the enemies that will end up in your lane is very difficult at low levels because your opponents likely won't know what the ideal is due to inexperience, so you should just probably focus on generic items.
Every team should have an Animal Courier and a set of Observer Wards at the start of every game purchased by the supports. 1Observer ward should be given to the offlane hero(or offlane heroes) to ward the pull camp of the enemy safe lane so they can't pull, or to give vision to prevent wrap around, and the other observer ward should be placed with vision of the rune so that your mid player has help knowing where the good rune is.
After that, items should be purchased from a mix of these items:
- Iron Branches
Ironwood branches are the best way to give your hero more mana and hp in the early game for a low cost. Most heroes will purchase Ironwood at the start of the game. - Tango (Comes with 4 per pack)
Every player in the game (with the exception of mid heroes sometimes) should purchase a tango set at the start of the game to ensure that their hp stays full enough until the buy a bigger regen item. You can give some your tangos to other people (called pooling Tangos) which lets them use it at a much reduced rate, so it's always fine to have extra tangos in a lane. - Healing Salve
Healing Salves will usually be purchased by offlane heroes and carries. Supports rarely buy them. - Clarity Potion
Clarity Potions are largely purchased by supports and some offlane heroes. Supports are often valued more for their ability to cast spells to harass, so I purchase at least 1 as a support. - Stout Shield
Stout Shield should be purchased by almost every melee carry, and often as a melee offlane hero. You will almost never need one as a ranged hero since it blocks less if you are a ranged hero. - Ring of Protection
Ring of Protection is a nice alternative to a Stout shield as a carry because it gives physical survivability and easily builds into a few different early game items like Ring of Basilius. Supports, if they have extra money, can purchase a Ring of Protectionearly to help them build Tranquil Boots. - Quelling Blade
Quelling Blade can be purchased by melee carries if they have trouble last hitting creeps, as the gold you gain from the last hits will pay for the item, and you'll jungle more rapidly later. Usually I don't purchase Quelling because stout is more important immediately, so buy it a few minutes later, especially if you are melee and plan to jungle a lot! - Smoke of Deceit
If I am playing support and I have extra money I'll purchase 1 smoke of deceit in case I want to gank. It makes you invisible to creeps and wards so it helps guarantee that you aren't spotted moving around the map to gank, at least by creeps orobserver wards. - Sentry Wards
I will rarely purchase sentry wards, but they are useful to help me deward enemy observer wards and spot invisible heroes. I will definitely purchase them if I'm against a Brood, Riki, or Bounty Hunter in my lane. There are 2 Sentries in every pack that you purchase.
If you are playing in the mid lane, you will often purchase one of these items:
- Null Talisman
Null is useful on Int heroes soloing mid because it provides you +9 damage which helps in last hitting versus your opponent, in addition to some other stats. - Wraith Band
Wraith Band is useful on Agi Heroes soloing mid because it provides you +9 damage which helps in last hitting versus your opponent, in addition to some other stats.
DO NOT GET BRACER IF YOU ARE A STR HERO. You cannot afford Tango+Bracer.
If you are playing in the Offlane, you will sometimes purchase:
- Boots of Speed
Boots are sometimes okay for an offlane hero because it gives you a tactical escape advantage over your opponents, who often have more damage and disable than you do, which requires you to be able to escape bad situations with multiple heroes. You will sometimes see supports purchase a boots so that they can bully offlane heroes or roam around the map, but I don't recommend that for new players.
If we summarize all of our early item purchases, we are purchasing stat items that give us slightly more HP, Mana, armor, and damage at the start of the game. We're purchasing regen items that help us stay in the lane longer, and we're buying some items that will help us build into items later in lane (Ring of Protection).
Here are some example starting item builds for each role in the game:
Carry:
- Stout
- Tango
- Salve
- Iron Branch
- Iron Branch
Mid:
- Wraith Band
- Tango
Offlane:
- Stout
- Tango
- Salve
- Iron Branch
- Clarity
Support 1:
- Courier
- Obs Ward
- Tango(x2)
- Clarity
Support 2(if reg support):
- Sentry
- Smoke
- Tango
- Iron Branch(x2)
- Clarity
Support 2(if melee jungler):
OR 
- Stout
- Ring of Protection (or Quelling Blade)
- Tango
What To Buy After Starting Gold
The items we purchase with our first gold once we start farming is a bit more diversified so I'll break it down by the role.
Carry
Carries will usually spend their first bit of gold on boots, finishing their Ring of Basilius, which gives them and their allies an armor and mana aura, purchasing Phase Boots or Treads after their initial boots, or Magic Sticks to help them get burst health and mana against offlane heroes. They can also purchase a regen item from the side shop like a Ring of Health, Helm of Iron Will, or Morbid Mask if it builds into an item that they need later.
Mid
Mid heroes very often will spend their first 700 gold on a Bottle since it gives them a huge amount of sustain in the mid lane due to runes. Afterward they will purchase a Boots of Speed and a Teleport Scroll so that they can gank to other lanes if needed, or teleport back to base in a dangerous situation.
Offlane
Offlane heroes purchase differently depending on how their lane is going. The first most important item is either boots or regen, depending on which one you need first.
For example, if you go to the offlane with a stout shield and 2 sets of regen (tango AND Salve), then you should be able to farm 450 gold for boots before you run out of regen. If you go to lane with Boots and 1 set of Tango, then you will probably need to purchaseTranquil Boots asap, which requires 550 gold[Ring of Protection (200), and Ring of Regen (350)]. You can also purchase a bottle as an offlane hero (700 gold), which is refillable at runes or base, if you have no desire to purchase Tranquil Boots on that hero.
Support
Support heroes will spend their first bit of money on a Flying Courier at 3:00 (when it's first available), getting TP scrolls to teleport to other lanes if needed, the next set of Observer wards at 4:50, and Boots when they get the farm. Other items they can purchase if they are doing extremely well are Arcane Boots, Tranquil Boots, Medallion, or pieces of an Urn of Shadows. All of those items have very inexpensive components that are useful early.
