Unless you have a 2h that allows you to consistently 1hko your mobs, use a 1handed. No point of using a slower weapon to 2hko mobs when you can 2hko them faster with a 1handed. 100%'d Red Katanas are your best friend from level 70-80. Having a Doombringer won't make much of a difference except for slowing down Soul Driver for the same outcome. You wont be very funded so just 100% scroll the Katana and you'll be 3hkoing jesters and 2hkoing them until level 80. Then 100% a Heaven's Gate and you'll be ohkoing Jesters at level 80? Then grind till level 90.
THEN, get a decent Devil's Sunrise at level 90, and you'll be 1hkoing Jesters and Galloperas.
Just remember, if you cant 1hko consistently, stick to the Katana.
EDIT: Also, people always rave about attack shields but realistically, they're a pretty penny and not many people can afford a decent one, let alone scroll one.
Once you get Adv Combo, it won't really matter what you use since it pretty much doubles you damage which is literally as if every monster had a weakness to Holy, but to those who do have weakness to Holy, you'll be doing like x4 damage, pretty fun. The speed from a 1h would be better.
The point where 1-handed truely excels over 2-handed is bossing. 2-handed swords have higher damage per hit, while 1-handed swords, being faster, have higher damage per minute. The differences won't really be all that big of a deal when training (especially if you're spamming Soul Driver, which kills pretty quickly), so in the end... the cheaper option is probably the better one.