It depends completely upon what you are using the times for.
- What precision do you need?
- How many will be stored? (On average / worst case)
Store as much precision as you need, but no more. (But also think about future needs). You don't save appointment times to the nearest nanosecond - it doesn't make sense. However if you are recording some type of data where very small intervals are important, then you might save it to the precision of the system clock (often 100 nanosecond chunks), or even a bit finer than that to allow for future versions with better clocks.
If you are only storing small numbers (say less than a few thousand) then storage size and access speed are probably unimportant. If you are storing many records, then the size of the records may become important.
Apart from the above considerations, it doesn't really matter; as long as it is clearly documented.
I'm not familiar with the sqlite db. Does it have any native date/time type? If so, that is probably simplest -- as long as it meets your requirements.