It is possible with the best analog rigs, to have stunning playback of your music with a background silence that is as quiet as digital. There is tape hiss on some old reissued masters, but the same noise appears on CD as well.
I am not saying that EVERY LP you own will be as dead silent as digitally recorded CD's, but many will be. I have LP's that were purchased not long after your first system in 1964, and most are dead quiet during playback.
Like anything mechanical, the differences between tables, tonearms and cartridges are enormous and set up is equally important. You can get excellent LP playback for a few hundred dollars, and the sky is the limit.