I suggest a whole new tower.
To step up to the 600mhz range your going to need a new processor, ram, motherboard, and if that new motherboard is ATX, your going to need a PS and maybe a new case too. Add in the fact that the vidcard/soundcard in that 150 are probably ancient, and you get the picture.
It would be better to start from scratch and put together a whole new system. As long as your getting a new CPU, its not going to make much sience to go lower than about 900, because prices level off. For example a 750 Duron = $34, a 800 = $35, 850 = $37, 900 = $38, 950 = $41 and a 1Ghz = $47. As you can see, its a matter of pennies of difference as they get slower.
As you can probably tell, i suggest going the Duron route. Its cheaper than a Celeron route, and much faster. If she doesnt play many games or much hard activity, i suggest pairing a 950 or 1Ghz duron with a KM133A motherboard like
This One. KM133A is an intergrated chipset, so you get build in sound and video, making things easier on you. If shes into games, you might want to get a ECS K7S5A and add in a medium power video card. If you want some good power and no fuss about Sound/Video/LAN for a LONG time, you can always spring for an nForce based board
like this one as they have all of that built in, althought there are deffinitly cheaper solutions out there.
I hope you get something that works well for you, Good luck!