HI i am about to do the main quest line, "Bleak falls Barrow" given by Faragar secret-fire to retreive the Dragon stone, now there also a concurrent quest called the "Golden Claw" given by Lucan Valerius in riverwood. to be retreived in retrieved in bleak falls barow also, which quest should i start first?

The golden Claw is half done just by doing the other quest.

Do both, collect both items in the barrow.

This is getting perilously close to spoilers, but the Golden Claw quest finishes quite quickly. Then keep going.

once you clear bleak falls barrow, you return to both people and your done both quests