I know almost nothing about record players. But if one has external connections to be plugged into a receiver, what makes one better than the other?
Records are cut to be played at specific speeds (usually 45 rpm or 33 1/3 rpm), so one factor is time-based errors. The belt drive system or direct drive system in the turntable needs to set a consistent accurate speed or else you will get skewed frequency response (so pitches can vary slightly up and down).
The cartridge (which holds the needle) is what runs inside of the groove of the vinyl and converts a mechanical pattern into an electrical signal via a magnetic system. This is attached to what is called the tone-arm--it is important for the needle to sit in the middle of the groove at a perpendicular angle (not pulling to one side or the other) and to be resting at the bottom of the groove with adequate pressure. If a cartridge isn't properly aligned and your tone arm is not set appropriately, this will also create a musical signal that is slightly off of what was intended by the cut of the vinyl. So, a quality cartridge and a well made + properly set tone-arm will help mitigate problems.
Also, vibrations from the turntable itself (particularly in direct-drive TTs) or from surrounding objects or even sound waves can affect the TTs performance subtly, as it can contribute to time-based errors and misalignment of the needle.