Flying out from an uncontrolled field, should I contact approach or departure at the nearby control field?
Approach and departure are two facets of the same facility, the TRACON, and it doesn't matter which you call, unless you're an IFR aircraft on an active flight plan or you have a flight plan on file that you want to activate.

For flight following, more important than picking between approach and departure frequencies, is to contact the TRACON on the frequency for the airspace that overlies your position.

For example, at Hollister, the TRACON is called "Norcal," and it handles dozens of different sectors, each with its own frequency. 



The frequency for approach and departure at Hollister are identical because that frequency is the arrivals frequency for San Jose International Airport (SJC). That's because Hollister is underneath the approach path for SJC, and that's whose radar screen you will pop up on.



What you should do is look up the frequency for your airport (or for a nearby airport) in the A/FD, in Airnav.com, or in your GPS database, and use that. If it has a discrete departure frequency, then you should probably use that, even though its for IFR departures, but for VFR, it doesn't really matter.