Hello there, my name is Balthazar and I plan on covering Destiny 2 content around here. With that introduction let's get into the build by starting off with the Subclass.

Subclass

Abilities

I recommend Rally Barricade for your Class Ability, if you play like me you probably won't be using it too actively during general PvE gameplay. Instead, I prefer to leave it charged and let it activate automatically via an exotic I will get into later.
For your melee, I recommend using Hammer Strike. For a basic build such as this. While Throwing Hammer spam is a rather effective build, I find it to be a boring playstyle that requires specific control settings. Instead, we'll grab Hammer Strike, it synergizes well with our chosen aspects and it can be used for some clutch movement if you need to save yourself in a pinch.
For the grenade, I'm just going to tell you to take Thermite Grenade. It is one of the strongest and most consistent grenades in the game. Four bursts of big damage in a long-range. If you need to clear out a bunch of Mobs then toss this at them.
For the super, I prefer Hammer of Sol. I just have better damage uptime with Hammer over Maul. It's mainly preference but Maul doesn't create a sunspot on use so.

Aspects

First Aspect we're taking Roaring Flames. It's a nice stacking damage bonus for your abilities that will help you burn through majors and ultras with your abilities alone. So while the stacking damage bonus is fantastic, another great aspect of this aspect is something they added in a patch a few weeks ago. While you have Roaring Flames buff your uncharged melee gains solar damage and has the ability to scorch enemies struck by it. Now there's a neat synergy between this aspect and Hammer Strike. With the way it works, unless you're sprinting for long enough, any melee is treated as an uncharged melee. Meaning that you gain the Solar damage even if Hammer Strike is charged.
For the second Aspect, we're taking Sol Invictus. Sunspots are simply one of the strongest abilities in the game, even after the nerfs. Solar ability kills creating spots of what is essentially Consecrated ground that heal you and damage enemies, while also giving you a little ability regen buff is simply fantastic. Not to mention this will help you keep basically 100% uptime on your restoration buff.

Fragments

First fragment slot I take Ember of Empyrean. While in this build it may not be the most impactful fragment, the benefit of it is that it helps us keep our restoration and radiant buffs when we may not be in a situation where we can safely reapply them.
For the second fragment, I grab Ember of Solace. If you were to swap out any fragment, I would start here. I mainly take this to help alleviate pressure in keeping up your buffs.
The third fragment is Ember of Searing. This simply helps you get your melee back quickly. Which helps keep your emergency movement up and helps synergize with our final fragment.
Final fragment slot I take Ember of Torches. It gives us the radiant buff which boosts our weapon damage by 25% in PvE. This can be triggered by Hammer Strike or Roaring Flames buffed melee so you should never have trouble keeping this up.

Gear

So the gear section is going to be pretty brief, I am working under the assumption you don't have a ton of perfect amazingly rolled gear. For basic builds at least.

Weapons

For primary weapons, I recommend the Sunshot exotic hand cannon if you want to run an exotic primary weapon. If you want to keep your exotic slot free would say take a nice Solar weapon like the Ogma PR6 or the Calus Mini-Tool.
For special it is really up to you, I usually roll with a shotgun, usually the Ragnhild-D craftable shotgun. But it is really your preference, specials are usually used for taking out Majors and Ultras.
For heavy it really depends on the type of content I'm doing. If it's more casual pressure-free content I like to run with a sword with Relentless Strikes and Whirlwind Blade. It's really efficient and great for damage. A pretty easy-to-get sword that can roll it is The Other Half from dares of Eternity. Now if the content is more serious or a sword isn't really feasible I take a Rocket launcher. Solid rocket launchers to look for are Bump in the Night and Palmyra-B.

Armor & Mods

For the Exotic armor piece for this build, I take Loreley Splendor. It's simply a strong really consistent exotic for Sunbreaker. Look for one with solid resilience and Restoration. This also benefits from the decreased cooldown of Rally Barricade.
For non-combat mods, I'm going to simply say use what goes with your gear. I usually use resilience mods to try and hit 100 resilience so I have that super quick Barricade cooldown.
For combat style mods I run with 1 Bountiful Wells, 2 Explosive Wellmakers, and 2 Melee Wellmakers. This gives you a lot of wells that will assist you in regening ability energy very quickly so you can have high uptime.

Conclusion

If you're just getting into the game or just starting a Titan and looking for a simple straightforward Sunbreaker build, this should give you a solid foundation. Thanks for reading and I hope this build serves you well.