Ok, I'll first start with the CustomPC budget build (copied out of the magazine) then give some general advice.
Budget PC, £522.53 inc VAT (I know, way over your budget, but this is for ideas)
Case: SilverStone PS02B Precision (£38.66)
Mobo: Gigabyte GA-H55M-UD2H (£80.37)
CPU: Intel Pentium G6950, 2.8x2Ghz (£74.78 - very cheap and incredibly overclockable)
RAM: 2x2GB Corsair XMS PC3-10666 (£100)
GFX: Gigabyte HD 5770 1GB (£131.59)
Cooling: Arctic Cooling Freezer 7 Pro Rev.2 (£16.32 - quieter and much more efficient than Intel stock)
PSU: Corsair CX400W (£34.55)
HDD: Samsung Spinpoint F3 320GB (£34.56 - 1TB is around £45, 1.5TB around £55 and 2TB around £88)
DVD: Samsung SH-D162D (£11.70 - might aswell get a DVD-RW for £4 extra)
Now obviously you can make a couple adjustments to the above build to shave off some costs. Again, this is for ideas, and this is the best build they recommend for price
erformance value.
If you want to save money, look for a motherboard with built in graphics. They'll suck, but they should still come above the minimum specs. You could try the Intel GMA that comes with Core i3/i5 but I don't know if SC2 and FF14 will support it. Possibly, but possibly not. At least it can play Borderlands... Anyway, by getting an IGP with the motherboard/CPU, it saves you money which you can save up until you have enough to get the GFX card of your dreams. Preferably HD 5770 minimum, although you'll still be fine with a HD 5670. I've not mentioned nVidia because they simply haven't made GPUs that can compete with ATI since the GeForce 9800 (which shared architecture with the next 2 generations of nVidia GPUs). They might have the edge in the laptop market with Optimus/330M, but in desktops ATI are simply better these days.
For the CPU, you
could go with an AMD CPU like the PhenomII X2 (don't bother with the X4/6 - you don't need the extra cores). I just find as a rule of thumb - AMD are 15-40% weaker compared to equivolently priced Intel CPUs.
For the PSU, you should be looking at the 400-500W range. And whatever PSU you pick, make sure it's from a good brand like Corsair or OCZ. Non-branded PSUs are electrical and fire hazards (and what would you expect for 1/3 of the price?).
HDD: Obviously you should only get as much as you need. I've got 2x1TB Samsung Spinpoint F1 in my computer and I'm practically out of space (shows how much music/games/anime I've got...). If you're more careful, 320GB will be fine (games rarely take more than 10GB anyway). In any case, they're cheap, and you can always get more as and when you need it - it'll even get cheaper/bigger by then!
RAM: 2GB minimum. 4GB maximum. Get Kingston, Corsair or OCZ. Most others aren't worth mentioning.
Windows: Not included in the price. I recommend getting a legit copy, but as a former student I know how helpful it can be to find other means of obtaining Windows to save yourself £90+ which can be better spent on a good GPU.
...Did I forget anything?