Hello and welcome to this fine forum.
Drake Sword is a great early weapon.
Ditch it when you're not satisfied with it's damage anymore.
If you're at Gaping Dragon, you can already make stronger weapons than the Drake Sword, but they'll require some farming.
In the Depths bonfire area, there are those creepy slime blob things. Those drop Large and Green titanite Shards. You can also find the Large Ember in the area with Butchers. Bring the Ember to the blacksmith Andre in Undead Parish and he will alow you to upgrade weapons to +10 and to Raw +5.
One fully upgraded weapon in these paths will require around 8-9 titanite Shards and 9 Large titanite Shards. It's safe to just go with 10 of each. You can buy the normal titanite Shards directly from Andre (800 Souls per one), or farm them from enemies in Undead Parish.
When you get there, upgrade the weapon/s of your choice to +10. Ignore Raw. Raw gives you some instant damage, but will be useless as you level up, while the +10 weapon can be later upgraded to +15 and will stay for you the entire game.
As for the weapons. When you open the weapons menu, you can see some stand alone letters below the damage numbers. Those are scaling letters. They start from "S" - being the best and end with "E" - being the lowest.Weapons scale with Strength, Dexterity, Intelligence and Faith, respectively, as the letters go. That means you're looking for a weapon that has at least C in the first letter field. Those are Strength weapons. If the weapon has the same letter in first two fields, you can use that as well. However, don't use weapons with letters in the last two fields as they require Intelligence, or Faith.
Good early weapons are the Mace (purchasable), Morning Star (hidden in Firelink Shrine), Reinforced Club (purchasable), Claymore (on the bridge with big red dragon), Zweihander (in the cemetery in the Firelink Shrine). After you beat the Gaping Dragon and venture forth, you will be able to farm Large Club and find Butcher Knife and Great Club, which are superb Str weapons.
If you manage to cut off Gaping Dragons tail, you will get a great Str weapon, but it will require a LOT of Str to use.
As for Stats.
Vitality raises your max HP.
Endurance raises the amount of things you can equip and remain agile and raises your Stamina.
Attunement raises the number of spells you can equip.
Strength is your muscles and is used to wield all weapons and to scale off with Str weapons, like Axes, Hammers and such.
Dexterity is your agility and works exactly like Strength, but for quick weapons, like Rapiers, Katanas and such.
Resistance is a joke of a stat that should never be raised, because it does nothing.
Intelligence allows you to use powerful spells and is used for weapon scaling.
Faith allows you to use Miracles, that heal and buff you and is used for weapon scaling.
Your stats depend on what you wish to make and what yu plan to do with your character further on. Most players focus on stopping on SL 100 for PvP, but since this is your first time, you should just enjoy the game and don't stress over details too much. If you really want to know. Most stats stop scaling efficiently at 40 with few exceptions. Those being Vitality, which stops being efficient at 50. As a Str character, you might want to go as far as to put 50 in Str as well. While this won't get you any extra damage, it will allow you to use all Str weapons with one hand, except for one (which isn't worth it).
I'm making a Str build for PvP as well and go with these stats.
Vit - 45
Att - 8
End - 40
Str - 50
Dex - 10
Res - 11
Int - 8
Faith - 8
You can try something like this as well, it will be good for PvE and PvP as well. ^^
Hope this helped you. Have fun with Dark Souls.
EDIT:
I intentionally avoided using links, even to our wiki, to eliminate the chances of spoilering the game for you.