The problem is if you don't trap NPC souls, you probably can't enchant any weapon with 1600 magicka since there aren't that many non-NPCs with grand souls.

Depends on your level. Lots of boss-level creatures reach Grand if your level is high enough.

Endless supply: Summon Gloom Wraith, or Summon Lich.

I don't want a grand soul to enchant with at 1st level. That would be too powerful. I usually do not even bother with enchanting anything until around 10th level or so. I want the game to be a challenge. I find it more fun that way. For the same reason, when I download armor or weapon mods, I make leveled lists of them, creating several versions of it that match the stats of vanilla gear. That way I am not using anything that is overpowered for my level.

The Uderfryke Matron has a grand soul regardless of level.

If you have the stones for it, you can stuff her into a grand soul gem at level one.

I must point out that I only recently learned this from our very own SubRosa.

Here's a list of creatures who provide reliable Grand souls:

Gloom Waiths
Goblin Warlords (note: can be leveled, but they do supply grand)
Liches (not the Nether variety)
Minotaur Lords
Rumare Slaughterfish Brood Mothers
The Underfrykte Matron
Xivilai

Umbra works even better as a sneak attack weapon as it has the among the highest base damage for one handed swords. The soultrap last long enough that you should be able to kill the enemy before it times out.
A spell with soul trap 2 sec and drain health 100 in on second is nice to finish of enemies.
The same spell can be used as an enchantment on a dagger.

I have used the house with the everscamps and umbra often to recharge equipment, four non agresive scamps in a house in Leyawiin who respawn in seconds.