For RAM vs cores, a typical rule of thumb in the VFX world is to have at least 2 GB of RAM for every physical core. So if you have 12 physical cores, you would want a minimum of 24 GB of RAM, but it's always a good idea to have more if you can afford it.
For the number of cores, Arnold tends to scale quite well on a high number of cores. Arnold has regular usage on machines that have anywhere from 4 physical cores to 128 physical cores, and for most scenes the speedup is fairly linear with the number of cores. Getting beyond about 14 cores you will need to use a multi-socket machine and have more than one physical CPU package, and most of the time that introduces no performance overhead with Arnold, but historically there have been situations where those types of machines suffered in per-core performance a little bit.
For Intel processors, just make sure you enable hyperthreading. That will appear to double your core count (from say 12 physical cores to 24 virtual cores). Arnold will usually perform about 20% faster with HT on, so a 12-core machine will perform approximately as if it had 14.4 cores, relatively speaking.
Most uses of Arnold will involve pulling data across a network (via NFS on Linux or a mapped drive on Windows). Get the fastest network connection and file servers you can, as these can have an outsized impact on startup time, and for texture-heavy scenes on overall render time. If, as you really should, you convert textures to .tx and/or use auto-tx in MtoA, HtoA, etc that will help mitigate a slower network or file server quite a bit if you can't avoid it otherwise.
