You'll get a nice two bed with that budget - in some areas you might even get a three bed, although most are nearer £700. Not sure that there will be many detached two beds in the areas you'll be looking at though - there are a greater number of them in the relatively newer housing areas which tend to be nearer the outskirts, like St Peters or Warndon Villages (both of which are generally nice areas but probably too far out for you) Should have no problem finding a two bed semi though.
I reckon you'll probably find what you're looking for in areas like St Johns (which is the same side of the river as the main uni campus), the Arboretum, the area around Barbourne/Gheluvelt Park or maybe Diglis/Cherry Orchard. London Road and Bath Road are two of the main residential roads on the way into town so you may have some luck there, although there are a lot of very big houses on those roads too.
Personally I'd give the Tolladine area a miss. From what you say about cars being torched I'm assuming you're in West Reading off the Oxford Road somewhere, and in my opinion Tolladine (Tolly to the locals) is comparable. A lot of the other areas are like Reading in that there are nice bits and not so nice bits but you'll probably get a feel for that when you view the properties.
I'd agree with your other half that Worcester is much more pleasant than Reading and if you've looked at any of my other posts you'll see I'm planning to move back there myself sometime in the not too distant future.
If you have any questions about particular roads that you see properties on then feel free to ask :)