Is ground noise really normal? If so, why?

Well white noise is a thing. Like pink noise only with more treble. Dead silent is a thing, its the complete absence of noise. Near is a thing. It means close but not quite there. So yeah I would say near dead silent white noise is a thing.

Sadly, hum is quite often the norm. It does not have to be! A properly set up system can be dead quiet, where all you hear is groove noise between songs.

Hum is a system-level issue, not due to any single component (unless it’s a crappy  design). Here is some more info:

http://www.hagtech.com/pdf/eliminatingnoise.pdf

Vinyl roar? Or hum?

I'd start by checking your interconnects are making good contact with the connectors on the TT and preamp (swap them out if you have spares), also check that the TT ground connector is securely connected to the preamp.
If the hum is still there then search up 'Ground Loops', it may be worth experimenting with ganging up all the mains plugs to a single wall socket if you haven't done that already.
Other than that I'd try to locate the source of the hum by disconnecting equipment until the hum goes away. Also check to see whether you have any equipment nearby that may be emitting interference.
The TT and preamp you reference look pretty high quality and I would not expect to hear any hum at all. The link provided by @hagtech looks like a good starting point.

Further to what @pragmasi said, ensure there are no routers, cable modems, or Wi-Fi units nearby. Move them with the volume up and note the change in hum levels.