Most modern audio electronics are designed to be linear. That means that ideally, it shouldn't matter how much signal level you have: the output level simply scales along with the input level, with no change in the signal quality.
In practice, that's never quite true. The most prominent factors are:
If you get over the clipping threshold, it... well, clips. In linear circuits based on operational amplifiers, this is a pretty yes-or-no situation, sounds very harsh, and is widely considered just wrong, so in your situation you should probably ensure clipping never happens.
In other applications, clipping is just part of the sound and can be desirable to drive a bit “hot”. In particular valve-based circuitry clips in a smooth way that enrichens the harmonics and compresses the signal, particularly desired for electric guitar. But for a turntable, any desired soft-clipping would presumably be already on the record – so even if using a tube preamp, significantly overdriving it would probably be counterproductive, unless you deliberately want to distort something.
Every piece of circuitry introduces some amount of noise (both Johnson-Nyquist white noise and various kinds of hum- or buzz interference). This is largely independent of the signal level, so it's typically best to keep the signal as high as possible in each stage of the signal chain, so you can turn the final output down and thereby reduce how much of the noise is audible in the end.
For these reasons, the standard practice is to turn the gain of each part of a signal chain up as high as possible so it just barely doesn't clip even at the loudest inputs. This can be achieved by putting in a loud input, turning up the gain until it just starts clipping, then turning down again by something like 3 dB to 9 dB. The more you take it down again, the more sure you can be that it really won't clip in action, but you will also pick up some more noise – though in your application that should hardly matter because a vinyl disc already has quite a high noise level that you can't possibly avoid no matter what gain settings you use.
Output levels, on devices that have controls for that, should generally be set to a reasonably high level too – either 100%, or to a 0 dB setting, or as high as the next device in the chain can handle without having to turn the gain knob extremely low (which could be problematic because it might get very sensitive to small variations and possibly unbalance the stereo).