Okay, enough of the training bashing.
To the OP, once you enter controlled airspace, the level of ATC service depends on the class of airspace.
You will always get an alerting and information service, plus:
Class A: Not allowed to enter VFR.
Class B: Both IFR and VFR is separated from IFR and VFR.
Class C: IFR is separated from IFR and VFR. VFR is separated from IFR. VFR will receive information about other VFR traffic as far as practical, with traffic avoidance on request.
Class D: IFR is separated from IFR. Other traffic will receive information about other traffic as far as practical, with traffic avoidance on request.
Class E is controlled for IFR, but uncontrolled for VFR. So for VFR ATSOCAS services apply.
Individual countries may put a slightly different twist on this, but this is more or less the ICAO standard.
The ATSOCAS (Air Traffic Service Outside Controlled Airspace) you know about. Basic, Traffic, whatnot. But these only apply to airspace that's uncontrolled (as far as VFR is concerned): E through G. So as your rightly found out, it doesn't make sense to ask for a "Basic service" when entering controlled airspace.
The ATSOCAS services (Basic, Traffic, whatnot) are typical UK exceptions to ICAO by the way. In other countries you should be asking for a "Flight Information Service" or any of the other ICAO compliant services.
If you want the details of what a country provides, both in uncontrolled and controlled airspace, look in their AIP. Typically sections ENR 1.2 and ENR 1.4.