Hi there, does she already have the 26in monitor - or is this something she will need to buy?
AFAIK, there are not many 26in monitors these days, mainly 24in and 27in ones and the odd 25in.
As for playing games, the size of the monitor doesn't really matter - instead it is the native resolution that is crucial. For a 26in monitor, I will assume that it's 1920x1080 resolution.
As for playing games - the onboard should be fine for playing flash games. However, if she tries anything remotely 3D (like the Sims 3) the unfortunately the HD 3000 graphics on that motherboard won't do too well.
For a cheap but good graphics card, then I would strongly suggest looking second hand. You can often get cards like the 8800GT, 9800GT, 9800GTX(+) or HD 4770, 4830 or 4850 for less than £40. If you must go for a new card, then the
HD 5570 should be enough - but in terms of graphics power it isn't a scratch on the second-hand cards mentioned above that can be had for similar money.