I see LittleFinger's lust of Sansa, more like him trying to redeem himself in his own eyes of failing to land Cathelyn and will woo the daughter instead. Littlefinger isn't stupid enough to marry her though, as he knows the wrath he'll incur with other seven kingdoms, therefore Sansa is a chesspiece for him to gain military alliances. Sansa is also using Littlefinger knowing that being sneaky, forging fake alliances and having a poker face keeps you alive and may give you the upper hand. This marriage of Sansa, will obviously be a sham, as Sansa detests the Boltons for betraying her father and brother, and seeing the old woman greet her, saying "The North remembers" means that her kinsfolks will side with her when the time comes.
It's sentimental for her, as her dad gave her the sword, plus Needle is her last belonging that remained of her Arya persona