Anyway, I got to the blacksmith in Anor Londo (took me ages to get past the two archers outside though) and I'm not sure what to do about weapon upgrades. I have a +10 Falchion which I could upgrade to lightning, but I the lightning spear I found in Sen's Castle didn't seem all that great to be honest. I've also heard that you can make unique weapons from the boss souls but maybe that's even later on? Finally, is the dragonslayer bow worth getting the stats for? I rarely use bows but it looks fun.
RE: Weapon upgrades. Elemental (lightning/fire) can be good, but the upgrade removes scaling to your stats. This is good in the first half of the game, but the more you level up, the worse off you are with elemental weapons. So it's always good to have a purely physical one to (which you will eventually want to take to the full +15.
There's no shortage of upgrade materials (except slabs) so upgrade your weapon to lightning and see how you like it, you can always buy/farm another weapon and keep that non-elemental. The lightning spear in Sen's isn't upgraded as is and spears don't do the best damage, so it's not the best barometer really.
RE: Weapon scaling. Look at the weapons own detailed stats, it tells you what letter grading each weapon scales with your own stats. Looking at the wiki your Falchion scales E with Strength, and B with Dex. That means when you level up STR and/or DEX you get a damage bonus with the weapon (that bonus is the +/- number at the side of the weapons damage number) - scale is E to A, then S which is the highest, so leveling up DEX will give a larger damage bonus with the Falchion. Elemental weapons remove this damage bonus completely - that's not a problem early on because your level isn't usually high enough to get a big enough bonus, but later on it will be, especially with a +15 weapon.