I've noticed a couple of differences between VFR departures in the Class D tower where I used to work compared to the Class B where I am now.
Class DPilot: "Spirit Ground, Cessna 172SP at Air Associates, information Delta, ready to taxi, VFR to the west."
ATC: "Cessna 172SP, Spirit Ground, runway 26R, taxi via Echo."
Pilot: "26R via Echo, Cessna 172SP."
We did handwritten strips for VFR departures and just had you depart on a 1200 squawk, and if you wanted flight following (or requested it on initial contact), the vast majority in the tower would just tell you that flight following would be on 126.5, which is STL Departure. Some of us started using the ARTS keyboard to enter VFR flight plans if you gave us a destination airport, but the older crew would chide us for it, saying that wasn't our job. I saw it as saving the Departure controller some time from having to enter it himself, and he would be able to see the info as soon as the target acquired on the radar (as well as receiving a printed VFR strip for that aircraft). I can also do a simple handoff of the radar target instead of Departure having to radar identify a plane.
Class BPilot: "St. Louis Clearance, Cessna 172SP at Signature, information Delta, request VFR departure (to the north, to Hannibal Airport, on a 350 degree heading)."
ATC: "Cessna 172SP, St. Louis Clearance, cleared out of the STL Class Bravo airspace to the north. Maintain VFR at 3000, departure frequency 119.15, squawk 4245."
Pilot: "Cessna 172SP, cleared out of Bravo to the north, maintain VFR at 3000, departure nineteen fifteen, squawk 4245."
ATC: "Cessna 2SP, readback correct. Advise ground on point niner ready to taxi."
Pilot: "Cessna 2SP, roger."
Pilot: "St. Louis Ground, Cessna 172SP at Signature, ready to taxi."
ATC: "Cessna 172SP, St. Louis Ground, runway 30R at Juliet intersection departure, taxi via Foxtrot, Juliet."
Pilot: "Cessna 172SP, 30R at Juliet via Foxtrot and Juliet."
For us at STL, if you request VFR departure, I create a flight plan in the FDIO that either has your destination airport or a fix in Departure's airspace (we have one that's north and one that's south of the airport, but you won't necessarily go to it, nor do we issue your clearance that way; it's simply a way for the radar controller to know what direction to expect you to fly). If you're going to an airport within Departure's airspace and at one of their controlled altitudes, I'll give you a local code on the ARTS computer. We have a reserved set of beacon codes for flights that originate and terminate within our airspace. Otherwise, I create a flight plan in the FDIO that gives you a code that's usable by the Center.
For us, if you don't tell us initially, we'll ask. If, on your initial call, you don't give the ATIS, I'll advise you which one's current; if you don't tell me where you're parked, I'll ask; and if you don't tell me if you're ready to taxi or not, I'll ask. "Cessna 2SP, ATIS Delta is current; where are you parked, and are you ready to taxi?"
My advice: Please just listen to the frequency before you give your life story. We typically combine Clearance, Flight Data, and Metering, and sometimes it gets combined with Ground (which has three frequencies of its own), so just because you hear silence doesn't necessarily mean I'm not listening to someone on another frequency. With the way our system works, if you call me on a different frequency than one on which I'm listening, I end up hearing both of you talk, and then I have to give the frustrated, "Say again," while telling you to standby. If the frequency sounds busy, keep it simple. If it's a quiet Saturday, feel free to shoot the breeze.