When it comes to "algo de", think of uncountable nouns (some water = algo de agua, some time = algo de tiempo, some energy = algo de energía, etc).
Just keep in mind that English uncountable nouns aren't necessarily uncountable in Spanish (for instance, we do count the bread (un pan, dos panes) and the furniture (un mueble, dos muebles).
"Algún" is used for countable nouns, say, things you can quantify using numbers (un perro, dos perros, tres perros).
Examples:
Algunos niños prefieren quedarse en casa / Some children prefer to stay at home
¿Hay algún doctor en esta sala? / Is there any doctor in this room?
Algún animal rompió el basurero / Some animal broke the trash can
You examples:
Tengo algo de dinero = I have some money
Tengo un poco dinero = I have a bit of money
Tengo algun dinero / this one sounds odd to me. I wouldn't say it, it's rather ungrammatical but I guess some natives may say in colloquial conversation.