Yes the Intel ones were terrible but this isn't Intel we're talking about, is it?
I have seen the integrated video and it is perfectly fine for the customer. You have to remember what he said: she does little, if any, gaming and isn't a power user so there won't be overclocking, there won't be the need for a GF4 Ti4200-128m or an ATI Radeon > 9200 etc.
I also have the SLK3700AMB and I recommend it to you for this system. I wanted it for the perfect blend of being a) aesthetically pleasing and (b) very useful/practical. It definitely succeeded on both. It looks great and has great quality not to mention it is QUIET! It has the option for a front 120mm fan and a rear 120mm fan. You could get a low-spinning 120mm fan to go with that system and provide very adequate cooling and yet also be very quiet. It also has rubber grommets and the like to use on HDs and CDROMs which totally silenced my system. I have a 2500+ in mine with a low-spinning 120mm in the front and a medium-spinning 120mm fan in the back and it is relatively quiet, yet the 2500+ OC'd to 2083MHz is at 103 F under load .
I would also recommend 2x256Mb PC2700/DDR333 from Crucial because it is VERY CHEAP and also of very high quality. You don't need PC3200, especially being that the FSB is not 400Mhz, but 333Mhz...so why bother? If she isn't a power user, she isn't going to care because we can all confirm that system will be a performer. Why buy what you don't need?
As far as monitors go, I would say to go for maybe a Viewsonic G70fb (or whatever that is) or the NEC's 17" SuperBright DiamondTron. I can't remember the model number, but I saw it in a Graphic Arts Lab once and it looked FANTASTIC. It is also guaranteed to be cheap, being that you could find a good 19" G90fb for her on Dell right now for $230.