You can go DEX STR or Quality (mix): I found the heide knight sword got me through to the Iron keep....(took it to +8 before switching?) where I picked up the others (Dex) below......
STR - Black Knight Greatsword - Greatsword - any other ultragreatsword.
DEX - Black Knight Halberd - katanas, Rickard's Rapier (early easy find at start of HUntsman's copse)., knives and curved swords are a little weak but with stone ring seem ALMOST viable....they suck on stone or steel bosses...so that's why I put BKH there first...you want to hit harder I guess, bring hurt with power, but also can bring hurt with stun lock?
Quality - you can actually do even better with the black knight weapons here also, but any of the old swords like claymore, bastard, Drangleic, etc work ok here...I cant recommend the claymore, too boring, just a preference, but its up to you.
The black knight weapons are solid, but really shine of you throw in a few INT and or FTH stats...the problem is finding the twinkling for them.
These are just sure fire recommendations, try branching out a bit and finding a unique weapon to upgrade...once you get the ability to upgrade better and get large shards and chunks you can upgrade whatever you want.