I think that Medion PC you linked to says it all, "Back to School PC Base Station", so it's probably not for you. Don't get me wrong, it's very good actually, but the graphics card won't be any good for the latest high-end games. An upgrade will help, but you may need to change the PSU. In the end all your 'upgrading' may cost more money in the long run than getting one proper system to begin with.
Looks like what you'll basically need is a:
1. High-end(ish) dual/quad-core CPU: or even an overclocked one - from what I know, Chillblast click here & Overclockers click here do these
2. Very good graphics card: performance-wise, don't go for anthing less than a HD 4870 / HD 4850 if you're on a tighter budget
3. Plenty of RAM: 4Gb should do for now - 2x2Gb modules, & a motherboard that has 4 RAM slots
4. 1Tb hard drive space: 2x500Gb SATAII / 500-750Gb if you think it'll be enough for now
5. Good, dedicated soundcard: from the Creative X-Fi range click here for example
6. Bigger budget than the Medion's £470: I'd say ~£700-1000 at the very least
Would you prefer XP to Vista or vice-versa?
If you're on a tighter budget, I'll have to suggest a lower spec. The kind of games played (going to be played) may determine how good a spec you can get for the money. G