Dungeons & Dragons always kind of hand-waved starting money. You just rolled it up. We can do better and create more interesting backgrounds for the heroes at the same time.

Fighter

1d12	Source
1	Stolen from a… (1d6: 1=relative; 2=church; 3=shop; 4=merchant; 5=evil merchant; 6=evil noble)
2-3	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
4-6	Earned… (1d6: 1=as a prison guard; 2=as a castle guard; 3-4=escorting trade caravans; 5-6=at war)
7-8	Won… (1d6: 1-2=in a legal dispute; 3-4=in a contest of strength and arms; 5-6=gambling)
9-10	Looted from a… (1d6: 1=random corpse; 2-4=barrow mound; 5-6=ruins)
11-12	Roll 1d10 twice; first is the bulk; second is the rest. Reroll duplicates.

Barbarian

Always roll twice. The first is the bulk; second is the rest. Reroll duplicates.

1d12	Source
1-2	Earned… (1d6: 1=as a sailor; 2-3=as a herder; 4-6=escorting trade caravans)
3	Legal payment (weregild) for the killing of a… (1d6: 1-2=sibling; 3-5=parent; 6=uncle)
4-7	Stolen in a raid of a… (1d6: 1=farm; 2=abbey; 3=town; 4=city; 5=ship; 6=castle)
8-9	Won… (1d6: 1-3=in a contest of strength and arms [roll again for the rest]; 4-6=gambling)
10-11	Looted from a… (1d6: 1=random corpse; 2-4=barrow mound; 5-6=ruins)
12	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)

Mage

1d12	Source
1	Stolen from… (1d6: 1=relative; 2=church; 3=shop; 4=merchant; 5=evil merchant; 6=evil noble)
2-3	Gifted from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
4-7	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
8	Won… (1d6: 1-2=in a legal dispute; 3-4=in a contest [roll again for the rest]; 5-6=gambling)
9-10	Looted from a… (1d6: 1=random corpse; 2-4=barrow mound; 5-6=ruins)
11-12	Roll 1d10 twice; first is the bulk; second is the rest. Reroll duplicates.

Thief & Bard

Always roll twice. The first is the bulk; second is the rest. Reroll duplicates.

1d12	Source
1-2	Earned… (1d6: 1=as a servant; 2-3=as an apprentice; 4-6=fencing stolen goods)
3	Looted from a… (1d6: 1-4=random corpse; 5=barrow mound; 6=ruins)
4-6	Stolen from a… (1d6: 1=relative; 2=church; 3=shop; 4=merchant; 5=evil merchant; 6=evil noble)
7-9	Won… (1d6: 1=in a legal dispute; 2-3=in a contest [roll again for the rest]; 4-6=gambling)
10-11	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
12	Gifted from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)

Cleric & Monk

1d12	Source
1	Won… (1d6: 1-2=in a legal dispute; 3-4=in a contest [roll again for the rest]; 5-6=gambling)
2-3	Gifted from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
4-7	Earned as a… (1d6: 1=mendicant; 2-3=church/temple servant; 4-6=healer)
8-9	Inherited from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
10	Looted from a… (1d6: 1=barrow mound; 2-4=evil temple; 5-6=ruins)
11-12	Roll 1d10 twice; first is the bulk; second is the rest. Reroll duplicates.

Druid

1d12	Source
1	Won… (1d6: 1-2=in a legal dispute; 3-4=in a contest; 5-6=gambling)
2-3	Gifted from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
4-7	Earned as a… (1d6: 1=mendicant; 2-3=church/temple servant; 4-6=healer)
8-9	Inherited from… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
10	Looted from a… (1d6: 1=barrow mound; 2-4=evil temple; 5-6=ruins)
11-12	Roll 1d10 twice; first is the bulk; second is the rest. Reroll duplicates.

Paladin

1d12	Source
1	Looted from a… (1d6: 1=barrow mound; 2-4=evil temple; 5-6=ruins)
2-3	Gifted from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
4-6	Won… (1d6: 1=in a legal dispute; 2-4=in a contest of arms; 5-6=gambling)
7-8	Earned… (1d6: 1=as a squire; 2-3=as a castle guard; 4-6=as spoils of war)
9-10	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
11-12	Roll 1d10 twice; first is the bulk; second is the rest. Reroll duplicates.

Ranger

Always roll twice. The first is the bulk; second is the rest. Reroll duplicates.

1d12	Source
1	Stolen from a… (1d6: 1=relative; 2=church; 3=shop; 4=merchant; 5=evil merchant; 6=evil noble)
2	Gifted from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)
3-6	Earned… (1d6: 1=as a herder; 2-3=as a castle guard; 4-6=escorting trade caravans)
7-8	Won… (1d6: 1-2=in a legal dispute; 3-4=in a contest of arms; 5-6=gambling)
9-10	Looted from a… (1d6: 1=random corpse; 2-4=barrow mound; 5-6=ruins)
11-12	Inherited from a… (1d6: 1=sibling; 2-4=parent; 5-6=family friend)