Pros:
Excellent Ganks
Great CC
Most of his damage Scales with HP
Very Tanky
Major assist in team fights
Not reliant on Blue

Cons:
Weak early game
Poor camp clear
Needs to farm a lot pre-6

Marks:
9 Attack Damage - Helps clear a bit faster

Seals:
9 Armor - Scales well with his W and helps for early survivability

Glyphs:
9 Scaling MR - Scales well with his W and the MR isn't needed early game but is excellent mid and late game.

Quints:
1 Armor - Scales well with his W and adds survivability
1 Attack Speed - to increase clear speed and helps with his passive proc
1 Attack Damage - Same as the Marks

Starting Items:
Ok these are fairly standard for Junglers. For the trinket just grab whichever one you will actually utilize.

First Back:
Again another standard buy when building a spirit item like the Spirit of Ancient Golem we will be buying later. Your first back you should DEFINITELY buy a ward, preferably a pink but if you can afford it grab a stealth.

Early Game:
Spirit Golem is a fantastic item on Braum for a few reasons, Tenacity, CDR, HP fo bonus damage from his Q and the conservation passive gold is definitely not substantial especially with his slow clear speed so its good to get as your first full item.

I usually get a Recurve Bow after the Spirit Golem to add extra clear speed as well as significantly increase the speed you activate your passive.

Core:
Giant's belt is always a safe grab when you are not sure what to get as it builds into Sunfire, Randuin and Warmog which are both fantastic items on him.

Usually I build the Sunfire first cuz honestly its just a good item. It helps deal damage both because of the extra HP for his Q and the...well fire damage for just being there. Armor is always good too.

OK now to talk about my favorite item on him! Wit's End! For a while I had looked for a good attack speed item on him and this is definitely the best one. The extra MR is good on its own but not to mention a lot of his damage is from the extra magic damage on his passive. when the stun hits you do extra magic damage then until the passive is back up on him you do extra magic damage with each basic. You will almost have full MR siphon by the time the stun first happens and then you have another 6-7 seconds to do bonus damage.

Boots:
Swiftness is my go to boots but Tabi is good if you are against attack speed champs and/or need the extra armor

Mid-Late Game:
From this point on the items you buy is greatly depending on what you are going against. Aegis/Locket are fantastic for MR and team support. Grab Frozen Heart against champions like Jinx, Jax and Fiora or any other Attack Speed champ. Grab a Randuin for more armor but not don't need the Aura from frozen heart, not to mention the bonus HP helps add some damage to his Q. For heavy poke champs grabbing a Banshee's Veil is solid. Warmog when going against mixed AP and AD champs and/or need good sustain.

If you need to build damage my usual go to items (even though defensive items are usually good enough for that) grabbing an Iceborn Gauntlet or Frozen Mallet.