The earliest one you can grab is Astora's Shortsword which in front of the sleeping undead dragon hanging from the cliffs if you take certain elevators down (master key unlocks the path right away). Pretty basic, fast, but a straight sword so its reach is not as amazing, and you will have to be content with smaller chunks of damage. It is the easiest of the bunch to get and if you are good at stick and move with straightswords in general, its a perfectly fine weapon.
GS of Artorias (non cursed version) comes from the Syf fight, and even gets a bonus against the Four Kings, but its split damage and the cursed version is really useful for the cursed ghost area. If you already blew through that area or willing to grind the curse items instead, GS of Artorias is one of the hardest hitting weapons in the game IF you build around it (balanced STR DEX INT and FAI), while the cursed version scales entirely off of STR and DEX as physical. I usually go with the cursed version, because slow weapons with wide swings are hard to use in the catacombs and the cursed version is a major convenience in the ghost area.
Last option is the Silver Knights Spear (the one I think I end up always using in the catacombs) which drops randomly off of silver knights in Ardo Londo (the spear version). The Spear is good because it has no faith reqs and is purely physical damage, plus its got huge reach. It wrecks shit down in the catacombs and is a solid weapon even outside of that specific area. In many of my runs I alternate this with the Moonlight Butterfly Spear, depending on what I am up against. The Ardo Londo Spear Knights are also a pretty easy and decent XP farm.
As for making your own, the initial divine ember is relatively easy to get early on. Its in the Divine Root Basin, just past the Moonlight Butterfly. That one will take you to +5 which is plenty for the Giants Tomb area. The second is a bitch, guarded by six of those fucking Giant Skeletons that make ER mobs look timid with their aggressiveness. If you go this route, take a weapon you like with decent damage output (Zweilhander is a favorite of mine for this) and slap it on there. I would not bother smithing up a standard weapon to use as a quick poker weapon in the Tomb, itself, as everything down there is rapey fast and hard hitting. Just get the Spear or Astorias for that job.