Ahoy Lothar,
From your post I can see that building it yourself is not an option

so you are going for a pre-built rig. Here are some hints that might help you:
- My current (3 years old) Pentium IV @2600 GHz with 2GB RAM and a 256MB ATI X800 runs GWX full detail, 16 Km visibility and all. So you should be fine with a modern PC, unless it is from the very lowest range.
- Key to performance is not the processor speed as you could think, but instead:
1.- Good overall transit of data (No "bottlenecks" caused by one cheaper component, like motherboard, video or RAM), i.e. a well balanced PC, and in that part the motherboard is ESSENTIAL. Look for one that admits faster processors and that allows the highest possible processor and RAM data output.
2.- A good videocard. Huge memory does not automatically mean higher performance, the chip speed matters a lot. NVidia are more stable, ATI have more performance for money, but do not render correctly some ffects in SH4.
3.- RAM. The more, the better. Even if your new PC can't run at all the speed the RAM admits, go for the higher spec RAM, as it will be later compatible with a processor upgrade. 2 GB should work marvels with GWX, but go for 1GB if costs skyrocket. Better 1GB of good memory now and a later upgrade, that 1,5 cheap GBs now.
When you are offered a PC, I would advice reading an internet review (Google search or go directly to Tom's hardware web) about at least: 1) Graphics card, and 2) Motherboard that comes shipped.
Finally, the integrated sound cards in many motherboards do a decent job, but they might become a bottleneck also when going for good performance in stressing games. Consider purchasing a dedicated Sound Card from Creative, and you will get better sounds plus performance.
Hope that helps, but in any case if you wish, post here the specs of the PC you are interested in, and we can help you evaluate it.