1. Carbon Composition
2. Carbon Film
3. Metal Film
4. Metal Oxide Film
This is a rather tough question. All have advantages and disadvantages, and will be suitable for different tasks. You might want to check out some online resources, for example
http://www.sasaudiolabs.com/theory10.htm.
Carbon composition resistors, for example, are not very stable, are noisy, exhibit voltage-dependent-resistance, yet are entirely non-inductive and can survive huge pulses (but can catch fire); they tend to sound very good and are great for vintage tube gear. Carbon films offer lower noise, and greater stability, however they exhibit greater inductance; they too can sound quite good (Riken / Kiwame, for example). Frankly I can't say much about metal types... they are less-noisy and more-stable than carbon ... But I don't use them in my vintage gear because they always brighten the sound up too much! I think these vary greatly by construction, so some research should be done before picking a metal resistor. For example, avoiding magnetic materials (steel leads, for example) in resistors is crucial for a good sound ... although I really don't understand why
Now, the really good stuff... tantalum resistors and bulk foil. Supposedly the best for audio, but prohibitively expensive. Since I won't spend $5-25 per resistor, I have never even bothered to try them.
Anyways, you'll also find that different resistors will sound good in different parts of a circuit. My advice would be to try standard carbon/metal film resistors (audio grade, non-inductive leads) first and then upgrade a few at a time that do important things (for example, those that provide loads, feedback, or carry a decent chunk of current) and see what floats your boat.
