Does anyone have a good or bad experience using a PC server rack for audio equipment?

The PC server rack will be just fine, and a really good solution frankly. Your system will benefit from a good rack, but I would not worry too much about overthinking it. I doubt vibration is an issue or ever would be unless you plan on running a turntable and you already have issues with this in the room.

I have long been a fan of rack mounting components. I know that some people are concerned about vibration issues but that has not been an issue for me. My gear is mounted in a 19-inch wood rack that I had made years ago. Most gear that's not available with rack ears can be fitted to rack mount - the folks at Middle Atlantic can almost always make it work. A component can sit on a rack shelf when that isn't practical.

Rack mounting prevents a lot of damage because components can't move. My cabling has just enough slack that I can roll the rack out from the wall and work from behind it as easily as from the front. That's a terrific convenience.

Thanks for the feedback.  It definitely will be more secure than what I have right now.

If vibration becomes an issue, you can always add something like the IsoAcoustics Gaia's to support the entire rack. Most racks come with threaded feet, so it is just a matter of replacing them with the weight-appropriate Gaia's. If the threads don't match IsoAcoustics is very accommodating and have a wide variety of threads available. If the rack's legs don't cooperate then you can always follow @mikhailark suggestion of building a platform.

That's a good idea, I am also thinking about some 4" rubber wheels, makes getting at the back of the equipment easier and also provides some portability.  Those are not major ticket items, just makes things more convenient.