I have a Lowrance Elite 4, color display with GPS in my primary fishing kayak. Mine is a a WS Ride135 Sit On Top, so there were unlimited mounting and rigging options for the finder. With a sit-in, you are going to have additional challenges and limitations to overcome. You'll either have to do a shoot-through-hull mount in an adhesive bed, or figure out some way to hang a contraption over the side to hold the transducer and manage the wires. As to the power supply, every finder I know of uses 12VDC. I use 3.5 amp-hour sealed lead acid AGM VRE batteries and get over a full day of use from one charge. I built a watertight battery box from a correctly sized snap-top tupperware box and it is velcro-d inside my hull.
I would not even consider a finder that does not have integrated GPS. Lowrance, Humminbird, and Garmin all make very good stuff.
To the simpleton, proof does not matter once emotion takes hold of an issue.