A general rule to know is that when you're counting physical entities, you'd almost always use native Korean.
For other quantities, it's better to remember what is counted in native and what is counted in sino-Korean. It might help to know that sino-Korean is used with counters associated with ordinality or ordinal numbers.
Counted in native Korean:
- Hours (for both telling time and duration)
- Months (only for duration)
- Number of physical objects
- Number of locations, people, types
Counted in sino-Korean:
- Minutes (for both telling time and duration)
- Months (only for dates)
- Years (for both telling time and duration)
- Numerals themselves in phone numbers, the number of a question on a test, etc..
Also, note that all Koreans switch to sino-Korean the moment the quantity exceeds 100. Although, in a few cases Koreans have mixed native and sino-Korean for numbers in that range. Some examples are 101, 백 하나, and 120, 백 스물.