The sample rate and word length are completely independent of converter quality.
The main factors that influence quality in current A/D converters are the analog conditioning circuit that feeds the converter chip, the quality of the power supply and supply decoupling, and appropriate circuit board layout. These are all based on well established engineering principles.
The A/D chips used in the "best" converters seem to come from a handful of semiconductor manufacturers, and in commercial quantities cost in the order of $10 each or less. Those very same converter chips are used in "pro" equipment at all price points.
In my opinion, your sample rate should be chosen on the basis of the intended use for the audio eg 44.1kHz for CD, 48kHz for video.
Higher sample rates were once advocated in order to move harmful sampling and filtering artefacts (aliasing) out of the audio band. However, current A/D conversion uses a technique called oversampling which samples the audio at a frequency well above the audio band and then uses a so-called decimation filter to yield digital audio at the desired sample rate. (Oversampling occurs at the low mega-Herz range in an exact multiple of the required sample rate). The analog filter only needs only limit the input signal bandwidth to be below the oversampling frequency. That means that the analog filter can be very simple and operate at the range of a few hundred thousand Herz - well outside the nominal audio range of 20kHz, and well out of harms way.
Conventional wisdom recommends to track and process audio at 24 bits, and then export / dither to 16 bits as required.
My opinion is 44.1KHz is perfectly adequate for high quality audio.
Paul