Oh gods, not again...
Sims 3 is going to be another WOW/Sims 2/Crysis. Every forum filled with requests for computers with the specific requirement that it "Must run Sims 3 really well"...
Not the OP's fault, as it's a fact of life that certain games will attract a crowd, but it's going to be a rough few months...
Anyway, I think a standard build for "basic gaming" would be:
AMD Athlon 7750+
AM2+ compatible m-ATX or ATX motherboard, doesn't need to be expensive.
2GB of DDR2 RAM
ATI Radeon 4670/4770/4830 (There is only a few quid difference, so I'd lean towards the lowest priced 4830)
SATA-II Hard Drive with 500GB of space and 32mb cache.
Whatever case your sister likes.
450-550w PSU (depends on the "Will I steal it off her next year and upgrade it?" chance)
You can get the 7750 and an m-ATX board for less than £100 now, so it's an obvious purchase. The list above doesn't include a screen or OS, which should add a hefty lift onto the price (although Ubuntu 9.10 is coming out soon... I liked that OS a lot, but you have to remember that it has two modes - it does absolutely everything you want it to do, but if you wanted it to do MORE... sudo became godlike.)
Make sure you include your sister in the case choice, unless it's a present.
- Huw
EDIT: PS, the build might seem overkill, but that system *will* run Sims 3 at 50+ FPS at all times, and will make a great workstation/movie player.