install hdtv to dvd/vcr recorder and cable box

I would suggest that you find a real custom installer that will know how to do this for you and guarantee that it will work. The electrician can run cables but will not likely know what it takes to get it to work.
The cable box will need to be connected via HDMI for you to get HD. The Panasonic DVD/VCR should be connected via HDMI, for best DVD playback, but may also need an additional connection for VCR playback. Some of these combo units will not output the VCR over HDMI or component video and will use a standard composite video/LR audio connection for videotapes. Check the owners manual or just try it.
I would suggest running a short HDMI cable from each to an automatic switcher that would be located at the remote location and run a long HDMI cable from it to the TV.
You may also need the additional 3 RCA cables for VCR playback.
Using the recorder will be problematical depending on what inputs it has and what outputs the cable box has. When you plug in the HDMI to the cable box it shuts off the component output but might leave the composite video and audio outputs active. If the recorder has this type of input then you can record but the timer function will not be useful unless the recorded has an ir emitter that can be programmed to change channels on the cable box. You won't be able to watch one channel and record another at the same time. A cable DVR makes time shifting much easier, has at least two tuners, and will be HD which the recorder will not.
If you are going to buy the equipment and cables yourself it is important you connect it together before the long HDMI cable is installed and make sure it works. Long HDMI cables can be tricky. An incompatible cable can just not work or be intermittent which is even more frustrating.
Don't forget that you will now have to control equipment in two locations so you will need an IR extension to make that comfortable to use.
A professional installer will set you up and make sure it all works. Worth the additional cost to have someone else to blame if there is a problem.