I've started new game with a spellsword character, but I don't know ,what is the best onehanded weapon to use. I have few suggestions:
-Bound sword/axe
-Dawnbreaker (good dmg, useful with undead, vizual effects, portable torch)
-Chillrend (very high dmg, high frost dmg, paralyze, vizual effects, dry ice)
-Dragonbane (high dmg, good against dragons)
-Harkon sword (good dmg, very good enchant, absorbs 15pts of health, stamina and magicka)
-Keening (good dmg, absorption 15pts of health, stamina and magicka, dwemer-tech, backstab)
-Blade of woe (very high dmg, absorbtion of health, backstab)
Or another weapon,what is the best for spellsword.
No no no no no none of this "what is the best" crap sir! A game like Skyrim is supposed to be immersive, it's not like other rpgs.
Just pick your favorite weapon, if it's stats are lacking you can just use smithing and enchanting. My favorite weapons are the Ghostblade and the Iron Sword, besides the fork, knife, steel and iron dagger there are no weaker weapons.
If you really need a "best" the best you could do is Harkon's Sword or make your own weapon with absorb magicka.
I would recommend taking any Weapon with any type of absorbing enchantments, it creates a nice synergy with magic as you don't really have any spells that allows you to absorb health, stamina or magicka, unless you're vampire, and if you're you can only absorb health anyway. So with that said, out of the ones you listed you should have the Blade of Woe, Keening or Harkon Sword. I think out of those 3 Keening is the superior weapon, because even though the enchantment is similar to Harkon's sword, they have the same damage input, and Keening is a dagger unlike Harkon's sword so you attack a lot faster. And the Blade of Woe only absorbs health while Keening absorbs all stats. So I say you go with Keening.
I was gonna go with Keening too but he's a spellsword, not a mage. Spellswords typicaly reply on their magic and power attacks to kill things. Keening is mostly a mage weapon, since most daggers can't stagger, plus its also quite heavy for a dagger so he'll have less power attacks.
I think it depends on the character, what point you're at in the game, and what spells you're using. Destruction? Alteration? Are you sneaking about and using illusion? Pick one that compliments whatever you've got going on in the other hand and your gameplay style. There are endless deadly combinations you can come up with.