OK, so as mentioned you first need to decide what you want from a camera and what you want to shoot, as well as whether you want to carry around the bulk of a larger camera and several lenses. After that you can narrow down the type of camera.
It is true that most cameras offer full manual control in terms of ISO, shutter and aperture, and many offer manual focus too. However, the ease in which you can access these controls differs greatly and so it is important that you try cameras out to see which suit you. Some cameras have menu based system to access ISO, aperture etc, some have dials on the body.
If you want to control depth of field in order to isolate the subject (such as in the classic portrait) then cameras with larger sensors will help achieve this, it is difficult (although not impossible) to do this with cameras such as your G16 as the sensor is very small, although not as small as your average compact camera. You can of course get compact cameras and bridge cameras with larger sensors such as the Sony RX100 and RX10 but these sensors are still smaller than the APS found in some DLSRs and CSCs, which are in turn smaller than the full frame sensors in other DSLRs and CSCs.
Finally, you do not need a DSLR to get full manual control with external dials, and large sensors. Mirrorless (aka Compact System Cameras) offer everything that a DLSR does, except tracking/continuous autofocus still can't match high end DSLRs. Cameras such as the Sony a6000 and Olympus OMD EM1 offer very good autofocus systems though that are not far off. Whilst the Olympus systems 'only' have a 4/3 sensor IQ is still superb, and it is possible to easily get very good subject isolation.