My main questions on this unit are 1. whether this warm up where no sound comes out is normal, and 2. whether it's worth performing other service after I get the cartridge in and it's complete (Gary from V-M recommended recapping the power board).
For question 2, 'worth' is an individual thing so I'll give you a few of my thoughts about it that might help you decide for yourself.
Different people have different goals with their projects. Some just want a functioning console, others want to remove what they like and make it into standalone piece that plays with other components, and still others want to use projects like this as test beds to learn and become familiar with repair/restoration so they can apply the knowledge to the next, and then the next projects. I see your console as a good candidate for the first of these (a console that will work), not a good candidate for the standalone piece, and a decent one for the learning process but it does have some quirks.
As consoles go, it is a 3 channel system (center channel for the bass) but it does so very economically with two small power tubes. Motorola made a few dozen configurations of their 3-channel consoles, and this one, while not the least powerful, is close to it. It does have a dedicated power transformer which is nice (it is not a "hot chassis" or transformerless design). On the plus side, it does have an FM Multiplexer which, as you commented, allows it to receive stereo FM. Many of the early consoles with stereo phonographs have only monophonic FM.
Your unit has the power amp, preamp and tuner all on one chassis, which could prove to get a bit tight to work on. It's kind of like a nice table radio, in a big box. But then it has a separate MPX unit (the HS996). If you do want to restore the system, you will want to make a note of the HS chassis number for the main unit, and get a schematic for it. Post it here and there is a chance that one of us already has it.
The level of servicing depends on how far you want to get into it. The main thing that we typically replace are the capacitors, as Gary correctly pointed out to you. We also test the resistors, measure voltages, clean the tube socket contact points, test the tubes, and some other stuff I am probably forgetting about. This requires some tools, good attention to details, willingness to read a schematic, etc. On the other hand, you might just get a can of contact cleaner, get at those dirty pots and see how it does. If it plays with no power supply hum you could use it as is. Of course it will live a longer, happier life if you do renew some components but this is where you get to make the call and decide for yourself.
The changer will require a different kind of service, and since you are already in touch with Gary, you've got low down on all things Voice of Music. He can get you the service manual and his step-by-step servicing instructions where the main objectives are to clean and regrease the mechanism, service the motor, and replace the rubber parts and the needle.
At best, though, these changers are mid-fidelity and while adequate, they are not intended to do what the better, magnetic cartridge tables that gained popularity a few years after this was made will do. This might or might not be a concern, though, as in many houses (like mine) there is a place where it fits in just fine. I don't expect it to be a critical-listening system, but throw on a stack of records and it's an instant party.
I hope this gives you some idea of how to proceed.
RWood