In my experience this works great -
First call: “XXX Approach, Bellanca 9578E VFR”
[this lets the controller know you are NOT a target he really needs to answer - and he can say, stand by, ignore you or respond “N9578E go ahead” -
Second Call: "Bellanca 9578E is XX miles [direction] from [USE A VOR or airport - and be CLOSE to the fix, inside 10 miles if possible] at 3500 climbing 5500, request flight following to XXX destination, if it is is NOT a major facility, phoenetically spell it for the controller - such as my base is IJD - say it them spell it, they don’t all the identifiers for the little fields, especially ones NOT in their sector!!!
The controller has EVERYTHING he needs in the second call - who, where, what and destination - he also gets, by adding that you are a 'Bellanca" - or whatever, the type of ac, which tells him performance. Telling him/her where you are and your altitude means, if you are reasonably accurate he may get your 1200 code and know EXACTLY where you are even before you get the beacon code.
THINK BEFORE YOU KEY THAT MIKE - know where you are and what you want to say. In 90% of the nation controllers may be working multiple sectors and you need to be brief and to the point, in busy sectors, if you want to get flight following you need to let the controller know with the first words out of your mouth that he is not dealing with somebody he might need to spend lots of time handholding. Life and time are too short to have to do that every day.
I am certain that in busy airspace sectors most controllers WANT to talk to VFR’s who are near departure or approach gates, overflying major airports outside the Classifed airspeace and just in general if they have time. If you are working an air carrier Class Charlie field and haev a gazillion VFR targets all squiawking 1200 you are working really hard to separate the IFR trafiice or at least give them warnings. If you are talking to the guys near your approach and departure gates, at least you know where they are going and what they’re doing.