Go for Sarranid Cav Sword if you want range, Nordic Champion for swing or Knightly Arming for stab dmg.
I think you missed the changes to the 1h weapons the patch brought:
Sarranid Cavalry Sword 5308 weight 1.35
requirement 8
spd rtng 95
weapon length 105
swing damage 33, cut
thrust damage 19 pierce
Nordic Champion's Sword 7842 weight 1.35
requirement 7
spd rtng 97
weapon length 102
swing damage 32, cut
thrust damage 21 pierce
Actually I preferred the sarranid guard sword more
Sarranid Guard Sword 4816 weight 1.25
requirement 6
spd rtng 99
weapon length 100
swing damage 30, cut
thrust damage 20 pierce
You trade in 3 cut damage and 5 range for 4 speed. From horseback, the damage you can deal in 1 hit is much more important than those 4 speed. Due to the damage bonus from the movementspeed, those 3 points in cut damage really do make a difference.
There's no reason to pick the NCS over the SCS when you intend to use it on horseback. I would advise you to bring a cheap secondary weapon for when you get dismounted, as the 95 speed on the SCS makes it terribad in melee. Something in the 1800-2500 gold range.
My gear would look like this (themed gear, you can pick whatever the hell you want obviously):
Steppe Horse 12645
Sarranid Cavalry Sword 5308
Round Cavalry Shield 2074 (or the elite cavalry shield depending on gear)
Sarranid Mail Shirt 5823
Sarranid Keffiyeh Helmet 1936
Leather Gloves 289
Sarranid Leather Boots 143
Total cost: 28218 gold.
A big bonus would be being able to manual block. In that case, the shield is only needed to catch arrows/blows while being mounted and you can put the shield away to negate the speedpenalty in melee. The 95 speed on the SCS makes it usuable without a shield, but a bit too slow with a shield imo. Footwork becomes very important if you do intend to use the SCS with a shield.
