
If you're not using magic then it's safe to consume. If you're a magic user you absolutely want trade this for one of the spells or miracles as each one is one of the heaviest hitting things in the game. The Dragon Demon Soul is likely the first archdemon soul you'll get (an area's final boss) as it's a puzzle based encounter rather then a true boss fight.
Can be traded for the Fireball spell from Sage Freke, the Firestorm spell from Yuria, the Witch, or the God's Wrath miracle from Saint Urbain. Dropped by the Dragon God in Stonefang Tunnel. It also doesn't scale so that initial high damage can ultimately be outpaced late game. As a result it'll take up a big chunk of your weight allowance, and require some timing to use well. The Dozer Axe looks great and has very high damage initially but it's massively heavy and slow. The Grey Demon Soul is probably one to eat early on for the souls. Can be given to Blacksmith Ed to ascend a Battle Axe +6 into the Dozer Axe. Dropped by the Vanguard in either the tutorial or the Shrine of Storms. The Lead Demon Soul is the first demon's soul you'll get in the game and unless you want the scraping spear it's probably fine to consume it for the souls.
Can be given to Blacksmith Ed in Stonefang Tunnel to ascend a Short Spear +7 into a Scraping Spear, which can reduce and enemy's equipment durability by 10 points per hit.Dropped by the Phalanx in the Boletarian Palace.
Note that most demon souls are a shame to consume, as most can be used to get unique upgrades/spells. You can have a look over here (where I got the list in the first place).
This is quite spoiler free, since you'd be hard pressed to know which demon yields which soul.
Storied Hero's Soul (or Traditional Hero's Soul): 4,000. Storied Soldier's Soul (or Traditional Soldier's Soul): 2,000. Souls you can just pick up from various places: