So as we all know Skyrim is full of stuff that belonged to the ancestors of people that live now, like Roggi's ancestral shield or Aegisbane, but ancestral weapon is very popular trope in fantasy in general, Trope maker is probably Arthurian legends but trope codifier has to be Narsil/Anduril from LOTR. Either way if you do not leave a sword behind for your descendants you pretty much failed as an adventurer, now there are many unique/special swords across Skyrim but personally i would like to RP my own sword that my character would leave to his descendants, the main reason is that all those other swords are part of someone else's legend, and my character would be just a footnote in it, i would like to make my own weapon with my own story behind it, i am kind of torn between Dwemer sword and Nord hero sword, both have qualities that make them a good candidate, Dwemer weapons don't rust or loose an edge, and they are made from mysterious alloy lost to time, kinda like Valarian steel from GOT, and in my mind, as time passes and more and more Dwemer metal gets lost so will remaining weapons become more prized. Nord hero sword on the other hand also has a nice ancient feeling to it, and while it is not as corrosion resistant as Dwemer metal anything that comes from Merethic era and survives well enough to still keep an edge rivaling present era blades is sure going to last for a few thousand years once repaired at Skyforge, and it already has Hero in it so that's a bonus, besides that not many people wield one of those so it would be easily recognizable.

I personally like the Katana swords,the "Blades" sword in Delphine's room at the Sleeping Giant Inn always ends up in my war chest as does "Dragonbane",from Sky Haven Temple. These are Akaviri weapons and as far as swords go,my favorites. After smithing Dragonbane up to about 70 dmg. I used it to kill Ancano at the CoW instead of trying to take him out with the Staff of Magnus. worked like a charm. If you are playing as "Dragon Born" I would think leaving Dragonbane as a legacy for your decendants would work well in a story line.

Again, someone else's story, Dragonbane was a known sword before my character got his hands on it, so in that regard you would just be one of the series of wielders, and i don't like the shape anyway, seems too unwieldy to me.

That being the case,having a sword that has no prior history,you pretty much have a blank palette to work with. I don't know anything about your character,his/her race,any "backstory" on the character? So your choice of weapon would be just that...YOUR choice. The dwemer weapons are kind of clunky looking to my eye but the Nord Hero stuff looks pretty good. Are you on console or PC? There are a lot of weapon mods available that would expand your choices for some cool swords.I use bows almost exclusively and I just added a mod called Better Bows that have some great looking weapons.Like to hear what you finally decide on!