Hello and welcome to Professor Reaperfan's class on casters in Demon's Souls, where we answer any and all questions pertaining to the use of magic!
For your stats, you will want to get your Intelligence to 40 for the maximum number of spell slots, and your Magic to at least 40. If you want to give up some survivability stats then you can also push your Magic to 50, it all comes down to personal choice really. Only get enough Endurance to wear some lightweight robes and still be able to fast roll, and put the rest of your points into Vitality.
You can get more spells by buying them from Freke, his apprentice, or Yuria in the Nexus. You will have to free Freke from his prison cell in 3-1 and Yuria from the tower in 1-3 before they will appear in the Nexus to teach you anything though. Freke and Yuria also have the ability to teach you very powerful spells if you give them the souls of certain bosses. The most important special boss soul spells you will want to be on the lookout for are:
Soul Ray - Give the Fool's Idol's soul (Doll Demon Soul) to Freke
Fireball - Give the Dragon God's soul to Freke
Homing Soul Arrow - Give the Old Monk's soul (Yellow Demon Soul) to Freke
Fire Spray - Give the Armor Spider's soul (Hard Demon Soul) to Freke
And when you get to your second playthrough after beating the game once, you should try to learn these spells:
Ignite - Give the Armor Spider's soul to Yuria
Firestorm - Give the Dragon God's soul to Yuria
Soulsucker - Give the Maiden in Black's soul to Yuria
The rest of the boss souls you can give to whomever you want, but I definitely reccomend using them to get more spells instead of consuming them for more souls.
As for upgrading your Crescent Falchion, you can do this by finding Darkmoonstone, though you will have to go to Blacksmith Ed in Stonefang since Boldwin in the Nexus can't upgrade with it. Darkmoonstone is found only in world 4, the Shrine of Storms. The local merchant in that world sells shards of it, but for chunks you will have to farm the Reapers and Crystal Lizards. And you must be very lucky to get a Pure Darmoonstone to upgrade the Falchion to its maximum upgrade, as only the Crystal Lizards in the Shrine of Storms drop it, and they only appear a limited number of times per playthrough.
Other equipment you will want to be on the lookout for are the Kris Blade, Old Monk's Headwraps, and Ring of Magical Sharpness. All of these items dramatically boost the power of your spells, though they also lower your defense against magic, so you may need to be a little more careful when using them. The Kris Blade is found in Stonefang, just before the elevator leading down to the Armor Spider on some catwalks. The Ring of Magical Sharpness is found in one of the Iron Maidens in the Prison of Hope in Latria. To get the Old Monk's Headwraps, you must invade someone in Latria and be summoned as the world's boss, then defeat the player.
Given that not many people are playing online right now, if you find yourself unable to invade for the Headwraps then the Silver Coronet also makes great headgear since it boosts your MP. Another note on equipment is that you should be using the Wooden Catalyst. Despite the fact that the Silver Catalyst gives you more MP, it is weaker and so reduces the power of your spells, and unless you dedicate your build to it then the Talisman of Beasts will usually be weaker as well. You may also try the Insanity Catalyst by using the Old Monk's soul to upgrade any other Catalyst, as even though it cuts your MP in half, it makes your spells much, much stronger. Though approach this option with caution, as having half your MP means you can only cast a few spells without having to stop and use some spice, and it also means you will be missing out on one of your most powerful spells, Homing Soul Arrow, until you play through New Game Plus and get another Yellow Demon Soul from the Old Monk.
Sorry if I was a bit wordy for you, but hopefully that answers most of your questions and future questions about casters. If you have any more please ask
EDIT: If you could tell me if your character is male or female then I could also let you know about which sets of robes/armor you should be on the lookout for