My poor Dalish never got to the part where I would have started thinking about this before I deleted him :/ My second character, Kail, a HN, used Starfang as soon as he got it and I like to pretend that he still had it during Witch Hunt -- that was *his* sword. Similar for my third character, another HN -- Cathal, who also kept using the Shield of Highever until Awakening, where he eventually settled for the Landsmeet Shield after cycling through some others. All of them had the Cousland Heraldry applied, though. He also cycled through swords and while he liked Vigilance, he prefers Starfang; I haven't really thought up a reason for him not having it in Awakening, though. Maybe he lend it to Zev or something.
My fourth and canon character, Shea, yet another HN, started using two handed swords after the Cousland massacre -- he'd been told they might suit him better before, but since Father preferred sword and shield, Shea had wanted to fight like that as well. After, in his mind, miserably failing to protect his family, he resolved to only fight at his best from now on and not let such sentiment pull him down (he still did plenty stuff out of sentiment, some of it plain stupid, though...) and switched to two handers, which he found to feel surprisingly natural and easy to use.
He kept the Chasind Flatblade until he got Yusaris, which became his default sword, though he switched to Ageless when there were a lot of Darkspawn around after acquiring it. He also used the Family Sword and Shield to fight Howe and always had them in the secondary weapon slot all the time.
Once he got Starfang post Landsmeet, he only used that; I think he might have chosen to leave it at home for Anora's protection while he was gone, it being a powerful one of a kind sword made by a master smith and all. He switched back to Yusaris (+ Ageless) until he got Vigilance, from which point on he only used that. It never meant as much to him as Starfang, though.
He also had a signature armour -- after getting Cailan's Armour post Landsmeet he put it on for the final battle and then kept all the way until the end of WH. A prince-consort needs kingly armour after all c;.
My fifth character, Evan Amell, doesn't have signature weapon -- he just uses whatever powerful staff he finds. He does have the Ancient Elven as his signature armour though. Similarly my sixth character, Dargan Aeducan, who is of the opinion that as long as weapon or armour is functional, it's good. ...Were he not a a dual-wielding rogue, he'd probably still use the Aeducan family shield, though. My seventh character, Farren Amell, is the same, but he'll have a thing for Starfang and Spellweaver. ...Not sure which I'll use yet. But that's more because he likes good swords, especially Longswords.
Cian Cousland on the other hand will never stop using the Family Sword, ever. Don't even think of trying to take it away or talking him into using something better. Family Sword it is. He'll likely like Starfang a lot, though, since it'll be his very own sword as opposed to being a memento and heirloom. He also has the ancient elven as his signature armour.
Geralt Caron, mage of the Orlesian variety (and somehow known to Anders from the Circle...), uses whatever is good and doesn't let sentimentality get in the way. I kind of want him to have an item very important to him, though... He's getting a backstory surprisingly quickly, especially considering that I made him on a whim and had never expected to ever even play an Orlesian :|